Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
[.,.] => [1] => [1] =>
[.,[.,.]] => [2,1] => [2,1] => 1
[[.,.],.] => [1,2] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => [3,2,1] => 11
[.,[[.,.],.]] => [2,3,1] => [2,3,1] => 01
[[.,.],[.,.]] => [1,3,2] => [3,1,2] => 10
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => 10
[[[.,.],.],.] => [1,2,3] => [1,2,3] => 00
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => 111
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,4,2,1] => 011
[.,[[.,.],[.,.]]] => [2,4,3,1] => [4,2,3,1] => 101
[.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,4,1] => 101
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,4,1] => 001
[[.,.],[.,[.,.]]] => [1,4,3,2] => [4,3,1,2] => 110
[[.,.],[[.,.],.]] => [1,3,4,2] => [3,4,1,2] => 010
[[.,[.,.]],[.,.]] => [2,1,4,3] => [2,4,1,3] => 010
[[[.,.],.],[.,.]] => [1,2,4,3] => [4,1,2,3] => 100
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1,4] => 110
[[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1,4] => 010
[[[.,.],[.,.]],.] => [1,3,2,4] => [3,1,2,4] => 100
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => 100
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => 000
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,3,2,1] => 1111
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,5,3,2,1] => 0111
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [5,3,4,2,1] => 1011
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [4,3,5,2,1] => 1011
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,4,5,2,1] => 0011
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [5,4,2,3,1] => 1101
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [4,5,2,3,1] => 0101
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [3,5,2,4,1] => 0101
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [5,2,3,4,1] => 1001
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [4,3,2,5,1] => 1101
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [3,4,2,5,1] => 0101
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [4,2,3,5,1] => 1001
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [3,2,4,5,1] => 1001
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [2,3,4,5,1] => 0001
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [5,4,3,1,2] => 1110
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [4,5,3,1,2] => 0110
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [5,3,4,1,2] => 1010
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [4,3,5,1,2] => 1010
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [3,4,5,1,2] => 0010
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [5,2,4,1,3] => 1010
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,4,5,1,3] => 0010
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [5,4,1,2,3] => 1100
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [4,5,1,2,3] => 0100
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [3,2,5,1,4] => 1010
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [2,3,5,1,4] => 0010
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [3,5,1,2,4] => 0100
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,5,1,3,4] => 0100
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [5,1,2,3,4] => 1000
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1,5] => 1110
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [3,4,2,1,5] => 0110
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [4,2,3,1,5] => 1010
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [3,2,4,1,5] => 1010
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [2,3,4,1,5] => 0010
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [4,3,1,2,5] => 1100
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [3,4,1,2,5] => 0100
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,4,1,3,5] => 0100
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [4,1,2,3,5] => 1000
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4,5] => 1100
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [2,3,1,4,5] => 0100
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [3,1,2,4,5] => 1000
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => 1000
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => 0000
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => 01111
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => 10111
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => 10111
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => 00111
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => 11011
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => 01011
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [4,6,3,5,2,1] => 01011
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => 10011
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => 11011
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => 01011
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => 10011
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => 10011
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => 00011
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => 11101
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => 01101
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => 10101
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => 10101
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => 00101
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [6,3,5,2,4,1] => 10101
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [3,5,6,2,4,1] => 00101
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => 11001
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => 01001
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [4,3,6,2,5,1] => 10101
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [3,4,6,2,5,1] => 00101
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [4,6,2,3,5,1] => 01001
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [3,6,2,4,5,1] => 01001
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => 10001
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => 11101
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => 01101
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => 10101
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => 10101
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => 00101
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => 11001
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => 01001
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [3,5,2,4,6,1] => 01001
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => 10001
>>> Load all 1840 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => 11001
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => 01001
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => 10001
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => 10001
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => 00001
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 11110
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [5,6,4,3,1,2] => 01110
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [6,4,5,3,1,2] => 10110
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [5,4,6,3,1,2] => 10110
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => 00110
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [6,5,3,4,1,2] => 11010
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [5,6,3,4,1,2] => 01010
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [4,6,3,5,1,2] => 01010
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [6,3,4,5,1,2] => 10010
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [5,4,3,6,1,2] => 11010
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [4,5,3,6,1,2] => 01010
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [5,3,4,6,1,2] => 10010
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [4,3,5,6,1,2] => 10010
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [3,4,5,6,1,2] => 00010
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [6,5,2,4,1,3] => 11010
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [5,6,2,4,1,3] => 01010
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [6,2,4,5,1,3] => 10010
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [5,2,4,6,1,3] => 10010
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,4,5,6,1,3] => 00010
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 11100
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [5,6,4,1,2,3] => 01100
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [6,4,5,1,2,3] => 10100
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [5,4,6,1,2,3] => 10100
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [4,5,6,1,2,3] => 00100
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [3,6,2,5,1,4] => 01010
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [3,2,5,6,1,4] => 10010
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [6,2,3,5,1,4] => 10010
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [2,3,5,6,1,4] => 00010
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [6,3,5,1,2,4] => 10100
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [3,5,6,1,2,4] => 00100
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [6,2,5,1,3,4] => 10100
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,5,6,1,3,4] => 00100
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 11000
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [5,6,1,2,3,4] => 01000
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [4,3,2,6,1,5] => 11010
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [3,4,2,6,1,5] => 01010
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [4,2,3,6,1,5] => 10010
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [3,2,4,6,1,5] => 10010
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [2,3,4,6,1,5] => 00010
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [4,3,6,1,2,5] => 10100
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [3,4,6,1,2,5] => 00100
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,4,6,1,3,5] => 00100
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [4,6,1,2,3,5] => 01000
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [3,2,6,1,4,5] => 10100
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [2,3,6,1,4,5] => 00100
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [3,6,1,2,4,5] => 01000
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,6,1,3,4,5] => 01000
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 10000
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 11110
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 01110
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => 10110
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => 10110
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => 00110
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => 11010
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [4,5,2,3,1,6] => 01010
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [3,5,2,4,1,6] => 01010
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => 10010
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => 11010
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => 01010
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => 10010
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => 10010
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => 00010
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => 11100
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [4,5,3,1,2,6] => 01100
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [5,3,4,1,2,6] => 10100
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [4,3,5,1,2,6] => 10100
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [3,4,5,1,2,6] => 00100
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [5,2,4,1,3,6] => 10100
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,4,5,1,3,6] => 00100
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => 11000
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [4,5,1,2,3,6] => 01000
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [3,2,5,1,4,6] => 10100
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [2,3,5,1,4,6] => 00100
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => 01000
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,5,1,3,4,6] => 01000
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 10000
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 11100
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => 01100
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => 10100
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => 10100
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => 00100
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => 11000
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [3,4,1,2,5,6] => 01000
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,4,1,3,5,6] => 01000
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 10000
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 11000
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => 01000
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 10000
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 10000
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1] => 011111
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [7,5,6,4,3,2,1] => 101111
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1] => 101111
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1] => 001111
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [7,6,4,5,3,2,1] => 110111
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [6,7,4,5,3,2,1] => 010111
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [5,7,4,6,3,2,1] => 010111
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [7,4,5,6,3,2,1] => 100111
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1] => 110111
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [5,6,4,7,3,2,1] => 010111
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [6,4,5,7,3,2,1] => 100111
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1] => 100111
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1] => 000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [7,6,5,3,4,2,1] => 111011
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [6,7,5,3,4,2,1] => 011011
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [7,5,6,3,4,2,1] => 101011
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [6,5,7,3,4,2,1] => 101011
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [5,6,7,3,4,2,1] => 001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [7,4,6,3,5,2,1] => 101011
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [4,6,7,3,5,2,1] => 001011
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [7,6,3,4,5,2,1] => 110011
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [6,7,3,4,5,2,1] => 010011
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [5,4,7,3,6,2,1] => 101011
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [4,5,7,3,6,2,1] => 001011
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [5,7,3,4,6,2,1] => 010011
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [4,7,3,5,6,2,1] => 010011
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [7,3,4,5,6,2,1] => 100011
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1] => 111011
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [5,6,4,3,7,2,1] => 011011
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [6,4,5,3,7,2,1] => 101011
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [5,4,6,3,7,2,1] => 101011
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [4,5,6,3,7,2,1] => 001011
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [6,5,3,4,7,2,1] => 110011
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [5,6,3,4,7,2,1] => 010011
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [4,6,3,5,7,2,1] => 010011
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [6,3,4,5,7,2,1] => 100011
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1] => 110011
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1] => 010011
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [5,3,4,6,7,2,1] => 100011
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1] => 100011
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1] => 000011
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [7,6,5,4,2,3,1] => 111101
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [6,7,5,4,2,3,1] => 011101
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [7,5,6,4,2,3,1] => 101101
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [6,5,7,4,2,3,1] => 101101
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [5,6,7,4,2,3,1] => 001101
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [7,6,4,5,2,3,1] => 110101
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [6,7,4,5,2,3,1] => 010101
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [5,7,4,6,2,3,1] => 010101
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [7,4,5,6,2,3,1] => 100101
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [6,5,4,7,2,3,1] => 110101
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [5,6,4,7,2,3,1] => 010101
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [6,4,5,7,2,3,1] => 100101
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [5,4,6,7,2,3,1] => 100101
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [4,5,6,7,2,3,1] => 000101
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [7,6,3,5,2,4,1] => 110101
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [6,7,3,5,2,4,1] => 010101
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [7,3,5,6,2,4,1] => 100101
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [6,3,5,7,2,4,1] => 100101
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [3,5,6,7,2,4,1] => 000101
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => 111001
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [6,7,5,2,3,4,1] => 011001
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [7,5,6,2,3,4,1] => 101001
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [6,5,7,2,3,4,1] => 101001
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [5,6,7,2,3,4,1] => 001001
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [4,7,3,6,2,5,1] => 010101
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [4,3,6,7,2,5,1] => 100101
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [7,3,4,6,2,5,1] => 100101
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [3,4,6,7,2,5,1] => 000101
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [7,4,6,2,3,5,1] => 101001
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [4,6,7,2,3,5,1] => 001001
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [7,3,6,2,4,5,1] => 101001
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [3,6,7,2,4,5,1] => 001001
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [7,6,2,3,4,5,1] => 110001
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [6,7,2,3,4,5,1] => 010001
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [5,4,3,7,2,6,1] => 110101
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [4,5,3,7,2,6,1] => 010101
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [5,3,4,7,2,6,1] => 100101
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [4,3,5,7,2,6,1] => 100101
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [3,4,5,7,2,6,1] => 000101
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [5,4,7,2,3,6,1] => 101001
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [4,5,7,2,3,6,1] => 001001
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [3,5,7,2,4,6,1] => 001001
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [5,7,2,3,4,6,1] => 010001
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [4,3,7,2,5,6,1] => 101001
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [3,4,7,2,5,6,1] => 001001
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [4,7,2,3,5,6,1] => 010001
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [3,7,2,4,5,6,1] => 010001
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => 100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => 111101
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [5,6,4,3,2,7,1] => 011101
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [6,4,5,3,2,7,1] => 101101
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [5,4,6,3,2,7,1] => 101101
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [4,5,6,3,2,7,1] => 001101
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [6,5,3,4,2,7,1] => 110101
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [5,6,3,4,2,7,1] => 010101
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [4,6,3,5,2,7,1] => 010101
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [6,3,4,5,2,7,1] => 100101
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [5,4,3,6,2,7,1] => 110101
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [4,5,3,6,2,7,1] => 010101
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [5,3,4,6,2,7,1] => 100101
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [4,3,5,6,2,7,1] => 100101
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => 000101
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [6,5,4,2,3,7,1] => 111001
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [5,6,4,2,3,7,1] => 011001
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [6,4,5,2,3,7,1] => 101001
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [5,4,6,2,3,7,1] => 101001
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [4,5,6,2,3,7,1] => 001001
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [6,3,5,2,4,7,1] => 101001
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [3,5,6,2,4,7,1] => 001001
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => 110001
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [5,6,2,3,4,7,1] => 010001
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [4,3,6,2,5,7,1] => 101001
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [3,4,6,2,5,7,1] => 001001
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [4,6,2,3,5,7,1] => 010001
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [3,6,2,4,5,7,1] => 010001
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => 100001
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => 111001
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1] => 011001
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [5,3,4,2,6,7,1] => 101001
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => 101001
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => 001001
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => 110001
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [4,5,2,3,6,7,1] => 010001
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [3,5,2,4,6,7,1] => 010001
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => 100001
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => 110001
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => 010001
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => 100001
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => 100001
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => 000001
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => 111110
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [6,7,5,4,3,1,2] => 011110
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [7,5,6,4,3,1,2] => 101110
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [6,5,7,4,3,1,2] => 101110
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [5,6,7,4,3,1,2] => 001110
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [7,6,4,5,3,1,2] => 110110
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [6,7,4,5,3,1,2] => 010110
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [5,7,4,6,3,1,2] => 010110
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [7,4,5,6,3,1,2] => 100110
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [6,5,4,7,3,1,2] => 110110
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [5,6,4,7,3,1,2] => 010110
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [6,4,5,7,3,1,2] => 100110
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [5,4,6,7,3,1,2] => 100110
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [4,5,6,7,3,1,2] => 000110
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [7,6,5,3,4,1,2] => 111010
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [6,7,5,3,4,1,2] => 011010
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [7,5,6,3,4,1,2] => 101010
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [6,5,7,3,4,1,2] => 101010
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [5,6,7,3,4,1,2] => 001010
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [7,4,6,3,5,1,2] => 101010
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [4,6,7,3,5,1,2] => 001010
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [7,6,3,4,5,1,2] => 110010
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [6,7,3,4,5,1,2] => 010010
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [5,4,7,3,6,1,2] => 101010
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [4,5,7,3,6,1,2] => 001010
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [5,7,3,4,6,1,2] => 010010
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [4,7,3,5,6,1,2] => 010010
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [7,3,4,5,6,1,2] => 100010
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [6,5,4,3,7,1,2] => 111010
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [5,6,4,3,7,1,2] => 011010
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [6,4,5,3,7,1,2] => 101010
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [5,4,6,3,7,1,2] => 101010
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [4,5,6,3,7,1,2] => 001010
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [6,5,3,4,7,1,2] => 110010
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [5,6,3,4,7,1,2] => 010010
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [4,6,3,5,7,1,2] => 010010
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [6,3,4,5,7,1,2] => 100010
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [5,4,3,6,7,1,2] => 110010
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [4,5,3,6,7,1,2] => 010010
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [5,3,4,6,7,1,2] => 100010
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [4,3,5,6,7,1,2] => 100010
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [3,4,5,6,7,1,2] => 000010
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [7,6,5,2,4,1,3] => 111010
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [6,7,5,2,4,1,3] => 011010
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [7,5,6,2,4,1,3] => 101010
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [6,5,7,2,4,1,3] => 101010
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [5,6,7,2,4,1,3] => 001010
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [7,6,2,4,5,1,3] => 110010
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [6,7,2,4,5,1,3] => 010010
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [5,7,2,4,6,1,3] => 010010
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [7,2,4,5,6,1,3] => 100010
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [6,5,2,4,7,1,3] => 110010
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [5,6,2,4,7,1,3] => 010010
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [6,2,4,5,7,1,3] => 100010
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [5,2,4,6,7,1,3] => 100010
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [2,4,5,6,7,1,3] => 000010
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => 111100
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [6,7,5,4,1,2,3] => 011100
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [7,5,6,4,1,2,3] => 101100
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [6,5,7,4,1,2,3] => 101100
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [5,6,7,4,1,2,3] => 001100
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [7,6,4,5,1,2,3] => 110100
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [6,7,4,5,1,2,3] => 010100
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [5,7,4,6,1,2,3] => 010100
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [7,4,5,6,1,2,3] => 100100
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [6,5,4,7,1,2,3] => 110100
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [5,6,4,7,1,2,3] => 010100
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [6,4,5,7,1,2,3] => 100100
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [5,4,6,7,1,2,3] => 100100
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [4,5,6,7,1,2,3] => 000100
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [7,3,6,2,5,1,4] => 101010
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [3,6,7,2,5,1,4] => 001010
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [3,7,2,5,6,1,4] => 010010
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [3,6,2,5,7,1,4] => 010010
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [3,2,5,6,7,1,4] => 100010
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [7,6,2,3,5,1,4] => 110010
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [6,7,2,3,5,1,4] => 010010
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [7,2,3,5,6,1,4] => 100010
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [6,2,3,5,7,1,4] => 100010
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [2,3,5,6,7,1,4] => 000010
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [7,6,3,5,1,2,4] => 110100
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [6,7,3,5,1,2,4] => 010100
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [7,3,5,6,1,2,4] => 100100
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [6,3,5,7,1,2,4] => 100100
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [3,5,6,7,1,2,4] => 000100
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [7,6,2,5,1,3,4] => 110100
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [6,7,2,5,1,3,4] => 010100
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [7,2,5,6,1,3,4] => 100100
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [6,2,5,7,1,3,4] => 100100
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [2,5,6,7,1,3,4] => 000100
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => 111000
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [6,7,5,1,2,3,4] => 011000
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [7,5,6,1,2,3,4] => 101000
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [6,5,7,1,2,3,4] => 101000
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [5,6,7,1,2,3,4] => 001000
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [4,3,7,2,6,1,5] => 101010
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [4,3,2,6,7,1,5] => 110010
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [3,4,7,2,6,1,5] => 001010
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [3,4,2,6,7,1,5] => 010010
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [4,7,2,3,6,1,5] => 010010
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [4,2,3,6,7,1,5] => 100010
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [3,7,2,4,6,1,5] => 010010
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [3,2,4,6,7,1,5] => 100010
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [7,2,3,4,6,1,5] => 100010
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [2,3,4,6,7,1,5] => 000010
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [4,7,3,6,1,2,5] => 010100
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [4,3,6,7,1,2,5] => 100100
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [7,3,4,6,1,2,5] => 100100
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [3,4,6,7,1,2,5] => 000100
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [7,2,4,6,1,3,5] => 100100
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [2,4,6,7,1,3,5] => 000100
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [7,4,6,1,2,3,5] => 101000
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [4,6,7,1,2,3,5] => 001000
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [3,7,2,6,1,4,5] => 010100
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [3,2,6,7,1,4,5] => 100100
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [7,2,3,6,1,4,5] => 100100
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [2,3,6,7,1,4,5] => 000100
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [7,3,6,1,2,4,5] => 101000
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [3,6,7,1,2,4,5] => 001000
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [7,2,6,1,3,4,5] => 101000
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [2,6,7,1,3,4,5] => 001000
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => 110000
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [6,7,1,2,3,4,5] => 010000
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [5,4,3,2,7,1,6] => 111010
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [4,5,3,2,7,1,6] => 011010
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [5,3,4,2,7,1,6] => 101010
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [4,3,5,2,7,1,6] => 101010
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [3,4,5,2,7,1,6] => 001010
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [5,4,2,3,7,1,6] => 110010
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [4,5,2,3,7,1,6] => 010010
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [3,5,2,4,7,1,6] => 010010
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [5,2,3,4,7,1,6] => 100010
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [4,3,2,5,7,1,6] => 110010
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [3,4,2,5,7,1,6] => 010010
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [4,2,3,5,7,1,6] => 100010
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [3,2,4,5,7,1,6] => 100010
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [2,3,4,5,7,1,6] => 000010
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [5,4,3,7,1,2,6] => 110100
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [4,5,3,7,1,2,6] => 010100
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [5,3,4,7,1,2,6] => 100100
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [4,3,5,7,1,2,6] => 100100
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [3,4,5,7,1,2,6] => 000100
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [5,2,4,7,1,3,6] => 100100
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [2,4,5,7,1,3,6] => 000100
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [5,4,7,1,2,3,6] => 101000
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [4,5,7,1,2,3,6] => 001000
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [3,2,5,7,1,4,6] => 100100
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [2,3,5,7,1,4,6] => 000100
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [3,5,7,1,2,4,6] => 001000
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [2,5,7,1,3,4,6] => 001000
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [5,7,1,2,3,4,6] => 010000
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [4,3,2,7,1,5,6] => 110100
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [3,4,2,7,1,5,6] => 010100
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [4,2,3,7,1,5,6] => 100100
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [3,2,4,7,1,5,6] => 100100
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [2,3,4,7,1,5,6] => 000100
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [4,3,7,1,2,5,6] => 101000
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [3,4,7,1,2,5,6] => 001000
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [2,4,7,1,3,5,6] => 001000
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [4,7,1,2,3,5,6] => 010000
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [3,2,7,1,4,5,6] => 101000
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [2,3,7,1,4,5,6] => 001000
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [3,7,1,2,4,5,6] => 010000
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [2,7,1,3,4,5,6] => 010000
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 100000
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 111110
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1,7] => 011110
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [6,4,5,3,2,1,7] => 101110
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1,7] => 101110
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => 001110
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [6,5,3,4,2,1,7] => 110110
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [5,6,3,4,2,1,7] => 010110
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [4,6,3,5,2,1,7] => 010110
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [6,3,4,5,2,1,7] => 100110
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1,7] => 110110
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1,7] => 010110
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [5,3,4,6,2,1,7] => 100110
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1,7] => 100110
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7] => 000110
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [6,5,4,2,3,1,7] => 111010
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [5,6,4,2,3,1,7] => 011010
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [6,4,5,2,3,1,7] => 101010
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [5,4,6,2,3,1,7] => 101010
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [4,5,6,2,3,1,7] => 001010
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [6,3,5,2,4,1,7] => 101010
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [3,5,6,2,4,1,7] => 001010
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [6,5,2,3,4,1,7] => 110010
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [5,6,2,3,4,1,7] => 010010
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [4,3,6,2,5,1,7] => 101010
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [3,4,6,2,5,1,7] => 001010
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [4,6,2,3,5,1,7] => 010010
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [3,6,2,4,5,1,7] => 010010
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => 100010
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => 111010
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1,7] => 011010
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [5,3,4,2,6,1,7] => 101010
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1,7] => 101010
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7] => 001010
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [5,4,2,3,6,1,7] => 110010
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [4,5,2,3,6,1,7] => 010010
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [3,5,2,4,6,1,7] => 010010
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [5,2,3,4,6,1,7] => 100010
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => 110010
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7] => 010010
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [4,2,3,5,6,1,7] => 100010
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => 100010
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => 000010
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => 111100
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [5,6,4,3,1,2,7] => 011100
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [6,4,5,3,1,2,7] => 101100
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [5,4,6,3,1,2,7] => 101100
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [4,5,6,3,1,2,7] => 001100
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [6,5,3,4,1,2,7] => 110100
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [5,6,3,4,1,2,7] => 010100
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [4,6,3,5,1,2,7] => 010100
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [6,3,4,5,1,2,7] => 100100
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [5,4,3,6,1,2,7] => 110100
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [4,5,3,6,1,2,7] => 010100
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [5,3,4,6,1,2,7] => 100100
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [4,3,5,6,1,2,7] => 100100
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [3,4,5,6,1,2,7] => 000100
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [6,5,2,4,1,3,7] => 110100
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [5,6,2,4,1,3,7] => 010100
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [6,2,4,5,1,3,7] => 100100
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [5,2,4,6,1,3,7] => 100100
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [2,4,5,6,1,3,7] => 000100
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => 111000
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [5,6,4,1,2,3,7] => 011000
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [6,4,5,1,2,3,7] => 101000
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [5,4,6,1,2,3,7] => 101000
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [4,5,6,1,2,3,7] => 001000
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [3,6,2,5,1,4,7] => 010100
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [3,2,5,6,1,4,7] => 100100
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [6,2,3,5,1,4,7] => 100100
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [2,3,5,6,1,4,7] => 000100
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [6,3,5,1,2,4,7] => 101000
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [3,5,6,1,2,4,7] => 001000
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [6,2,5,1,3,4,7] => 101000
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [2,5,6,1,3,4,7] => 001000
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => 110000
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [5,6,1,2,3,4,7] => 010000
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [4,3,2,6,1,5,7] => 110100
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [3,4,2,6,1,5,7] => 010100
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [4,2,3,6,1,5,7] => 100100
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [3,2,4,6,1,5,7] => 100100
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [2,3,4,6,1,5,7] => 000100
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [4,3,6,1,2,5,7] => 101000
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [3,4,6,1,2,5,7] => 001000
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [2,4,6,1,3,5,7] => 001000
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [4,6,1,2,3,5,7] => 010000
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [3,2,6,1,4,5,7] => 101000
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [2,3,6,1,4,5,7] => 001000
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [3,6,1,2,4,5,7] => 010000
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [2,6,1,3,4,5,7] => 010000
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 100000
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 111100
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7] => 011100
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [5,3,4,2,1,6,7] => 101100
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7] => 101100
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => 001100
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [5,4,2,3,1,6,7] => 110100
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [4,5,2,3,1,6,7] => 010100
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [3,5,2,4,1,6,7] => 010100
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => 100100
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => 110100
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7] => 010100
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [4,2,3,5,1,6,7] => 100100
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => 100100
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => 000100
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => 111000
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [4,5,3,1,2,6,7] => 011000
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [5,3,4,1,2,6,7] => 101000
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [4,3,5,1,2,6,7] => 101000
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [3,4,5,1,2,6,7] => 001000
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [5,2,4,1,3,6,7] => 101000
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [2,4,5,1,3,6,7] => 001000
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => 110000
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [4,5,1,2,3,6,7] => 010000
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [3,2,5,1,4,6,7] => 101000
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [2,3,5,1,4,6,7] => 001000
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [3,5,1,2,4,6,7] => 010000
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [2,5,1,3,4,6,7] => 010000
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 100000
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 111000
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7] => 011000
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => 101000
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => 101000
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => 001000
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => 110000
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [3,4,1,2,5,6,7] => 010000
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [2,4,1,3,5,6,7] => 010000
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 100000
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 110000
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => 010000
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 100000
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 100000
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [7,8,6,5,4,3,2,1] => 0111111
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => [8,6,7,5,4,3,2,1] => 1011111
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [7,6,8,5,4,3,2,1] => 1011111
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [6,7,8,5,4,3,2,1] => 0011111
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => [8,7,5,6,4,3,2,1] => 1101111
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => [7,8,5,6,4,3,2,1] => 0101111
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => [6,8,5,7,4,3,2,1] => 0101111
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [5,6,8,7,4,3,2,1] => [8,5,6,7,4,3,2,1] => 1001111
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [7,6,5,8,4,3,2,1] => 1101111
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [6,7,5,8,4,3,2,1] => 0101111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => [7,5,6,8,4,3,2,1] => 1001111
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [6,5,7,8,4,3,2,1] => 1001111
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [5,6,7,8,4,3,2,1] => 0001111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => [8,7,6,4,5,3,2,1] => 1110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [4,7,8,6,5,3,2,1] => [7,8,6,4,5,3,2,1] => 0110111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => [8,6,7,4,5,3,2,1] => 1010111
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => [7,6,8,4,5,3,2,1] => 1010111
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [5,4,8,7,6,3,2,1] => [8,5,7,4,6,3,2,1] => 1010111
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [5,4,7,8,6,3,2,1] => [5,7,8,4,6,3,2,1] => 0010111
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => [8,7,4,5,6,3,2,1] => 1100111
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [6,5,4,8,7,3,2,1] => [6,5,8,4,7,3,2,1] => 1010111
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [5,6,4,8,7,3,2,1] => [5,6,8,4,7,3,2,1] => 0010111
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => [6,8,4,5,7,3,2,1] => 0100111
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => [8,4,5,6,7,3,2,1] => 1000111
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [7,6,5,4,8,3,2,1] => 1110111
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => [6,7,5,4,8,3,2,1] => 0110111
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => [7,5,6,4,8,3,2,1] => 1010111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [6,5,7,4,8,3,2,1] => 1010111
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => [5,6,7,4,8,3,2,1] => 0010111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => [7,6,4,5,8,3,2,1] => 1100111
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => [6,7,4,5,8,3,2,1] => 0100111
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => [5,7,4,6,8,3,2,1] => 0100111
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => [7,4,5,6,8,3,2,1] => 1000111
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => [6,5,4,7,8,3,2,1] => 1100111
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => [5,6,4,7,8,3,2,1] => 0100111
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => [6,4,5,7,8,3,2,1] => 1000111
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => [5,4,6,7,8,3,2,1] => 1000111
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [4,5,6,7,8,3,2,1] => 0000111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => [8,7,6,5,3,4,2,1] => 1111011
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => [7,8,6,5,3,4,2,1] => 0111011
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => [8,6,7,5,3,4,2,1] => 1011011
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => [7,6,8,5,3,4,2,1] => 1011011
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => [8,7,5,6,3,4,2,1] => 1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => [7,8,5,6,3,4,2,1] => 0101011
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [3,5,6,8,7,4,2,1] => [8,5,6,7,3,4,2,1] => 1001011
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [3,7,6,5,8,4,2,1] => [7,6,5,8,3,4,2,1] => 1101011
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [3,6,7,5,8,4,2,1] => [6,7,5,8,3,4,2,1] => 0101011
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [3,6,5,7,8,4,2,1] => [6,5,7,8,3,4,2,1] => 1001011
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => [5,6,7,8,3,4,2,1] => 0001011
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => [8,7,4,6,3,5,2,1] => 1101011
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [4,3,6,8,7,5,2,1] => [8,4,6,7,3,5,2,1] => 1001011
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => [4,6,7,8,3,5,2,1] => 0001011
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => [8,7,6,3,4,5,2,1] => 1110011
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [3,4,7,8,6,5,2,1] => [7,8,6,3,4,5,2,1] => 0110011
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [3,4,6,8,7,5,2,1] => [8,6,7,3,4,5,2,1] => 1010011
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [3,4,7,6,8,5,2,1] => [7,6,8,3,4,5,2,1] => 1010011
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => [6,7,8,3,4,5,2,1] => 0010011
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => [5,8,4,7,3,6,2,1] => 0101011
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => [5,4,7,8,3,6,2,1] => 1001011
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [4,5,3,8,7,6,2,1] => [8,4,5,7,3,6,2,1] => 1001011
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [4,5,3,7,8,6,2,1] => [4,5,7,8,3,6,2,1] => 0001011
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [3,5,4,8,7,6,2,1] => [8,5,7,3,4,6,2,1] => 1010011
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [3,5,4,7,8,6,2,1] => [5,7,8,3,4,6,2,1] => 0010011
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [4,3,5,8,7,6,2,1] => [8,4,7,3,5,6,2,1] => 1010011
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => [4,7,8,3,5,6,2,1] => 0010011
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => [8,7,3,4,5,6,2,1] => 1100011
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [3,4,5,7,8,6,2,1] => [7,8,3,4,5,6,2,1] => 0100011
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => [6,5,4,8,3,7,2,1] => 1101011
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [5,6,4,3,8,7,2,1] => [5,6,4,8,3,7,2,1] => 0101011
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [4,6,5,3,8,7,2,1] => [6,4,5,8,3,7,2,1] => 1001011
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => [4,5,6,8,3,7,2,1] => 0001011
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => [4,6,8,3,5,7,2,1] => 0010011
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [3,4,6,5,8,7,2,1] => [6,8,3,4,5,7,2,1] => 0100011
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [4,5,3,6,8,7,2,1] => [4,5,8,3,6,7,2,1] => 0010011
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [3,5,4,6,8,7,2,1] => [5,8,3,4,6,7,2,1] => 0100011
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [4,3,5,6,8,7,2,1] => [4,8,3,5,6,7,2,1] => 0100011
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [3,4,5,6,8,7,2,1] => [8,3,4,5,6,7,2,1] => 1000011
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,8,2,1] => 1111011
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => [6,7,5,4,3,8,2,1] => 0111011
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => [7,5,6,4,3,8,2,1] => 1011011
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [6,5,7,4,3,8,2,1] => [6,5,7,4,3,8,2,1] => 1011011
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [5,6,7,4,3,8,2,1] => 0011011
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [4,6,7,5,3,8,2,1] => [6,7,4,5,3,8,2,1] => 0101011
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [5,4,7,6,3,8,2,1] => [5,7,4,6,3,8,2,1] => 0101011
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [4,5,7,6,3,8,2,1] => [7,4,5,6,3,8,2,1] => 1001011
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => [6,5,4,7,3,8,2,1] => 1101011
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [4,6,5,7,3,8,2,1] => [6,4,5,7,3,8,2,1] => 1001011
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,8,2,1] => 1001011
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [4,5,6,7,3,8,2,1] => 0001011
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [3,7,6,5,4,8,2,1] => [7,6,5,3,4,8,2,1] => 1110011
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [4,3,6,7,5,8,2,1] => [4,6,7,3,5,8,2,1] => 0010011
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1] => [7,6,3,4,5,8,2,1] => 1100011
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [5,4,3,7,6,8,2,1] => [5,4,7,3,6,8,2,1] => 1010011
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [4,5,3,7,6,8,2,1] => [4,5,7,3,6,8,2,1] => 0010011
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [3,5,4,7,6,8,2,1] => [5,7,3,4,6,8,2,1] => 0100011
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => [4,7,3,5,6,8,2,1] => 0100011
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [3,4,5,7,6,8,2,1] => [7,3,4,5,6,8,2,1] => 1000011
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [6,5,4,3,7,8,2,1] => 1110011
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => [4,5,6,3,7,8,2,1] => 0010011
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => [6,5,3,4,7,8,2,1] => 1100011
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [4,3,6,5,7,8,2,1] => [4,6,3,5,7,8,2,1] => 0100011
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => [6,3,4,5,7,8,2,1] => 1000011
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [5,4,3,6,7,8,2,1] => 1100011
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [3,5,4,6,7,8,2,1] => [5,3,4,6,7,8,2,1] => 1000011
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,8,2,1] => 1000011
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [3,4,5,6,7,8,2,1] => 0000011
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => [8,7,6,5,4,2,3,1] => 1111101
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => [7,8,6,5,4,2,3,1] => 0111101
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => [8,6,7,5,4,2,3,1] => 1011101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [2,7,6,8,5,4,3,1] => [7,6,8,5,4,2,3,1] => 1011101
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [2,5,8,7,6,4,3,1] => [8,7,5,6,4,2,3,1] => 1101101
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [2,6,5,8,7,4,3,1] => [6,8,5,7,4,2,3,1] => 0101101
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [2,5,6,8,7,4,3,1] => [8,5,6,7,4,2,3,1] => 1001101
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [2,7,6,5,8,4,3,1] => [7,6,5,8,4,2,3,1] => 1101101
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [2,6,7,5,8,4,3,1] => [6,7,5,8,4,2,3,1] => 0101101
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [2,5,7,6,8,4,3,1] => [7,5,6,8,4,2,3,1] => 1001101
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => [5,6,7,8,4,2,3,1] => 0001101
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => [8,7,6,4,5,2,3,1] => 1110101
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => [8,6,7,4,5,2,3,1] => 1010101
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [2,5,4,8,7,6,3,1] => [8,5,7,4,6,2,3,1] => 1010101
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [2,4,5,7,8,6,3,1] => [7,8,4,5,6,2,3,1] => 0100101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => [6,5,8,4,7,2,3,1] => 1010101
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => [6,8,4,5,7,2,3,1] => 0100101
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [2,4,5,6,8,7,3,1] => [8,4,5,6,7,2,3,1] => 1000101
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => [7,6,5,4,8,2,3,1] => 1110101
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [2,5,7,6,4,8,3,1] => [7,5,6,4,8,2,3,1] => 1010101
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [2,6,5,7,4,8,3,1] => [6,5,7,4,8,2,3,1] => 1010101
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [2,4,6,7,5,8,3,1] => [6,7,4,5,8,2,3,1] => 0100101
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => [4,5,6,7,8,2,3,1] => 0000101
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => [8,7,6,3,5,2,4,1] => 1110101
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [3,2,6,8,7,5,4,1] => [8,6,7,3,5,2,4,1] => 1010101
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [3,2,7,6,8,5,4,1] => [7,6,8,3,5,2,4,1] => 1010101
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [3,2,5,8,7,6,4,1] => [8,7,3,5,6,2,4,1] => 1100101
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [3,2,6,5,8,7,4,1] => [6,8,3,5,7,2,4,1] => 0100101
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [3,2,7,6,5,8,4,1] => [7,6,3,5,8,2,4,1] => 1100101
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [3,2,6,5,7,8,4,1] => [6,3,5,7,8,2,4,1] => 1000101
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [3,2,5,6,7,8,4,1] => [3,5,6,7,8,2,4,1] => 0000101
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => [8,7,6,5,2,3,4,1] => 1111001
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [2,3,6,8,7,5,4,1] => [8,6,7,5,2,3,4,1] => 1011001
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [2,3,7,6,8,5,4,1] => [7,6,8,5,2,3,4,1] => 1011001
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => [6,7,8,5,2,3,4,1] => 0011001
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [2,3,5,8,7,6,4,1] => [8,7,5,6,2,3,4,1] => 1101001
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [2,3,5,7,8,6,4,1] => [7,8,5,6,2,3,4,1] => 0101001
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => [8,5,6,7,2,3,4,1] => 1001001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [2,3,7,6,5,8,4,1] => [7,6,5,8,2,3,4,1] => 1101001
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [2,3,6,7,5,8,4,1] => [6,7,5,8,2,3,4,1] => 0101001
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [2,3,6,5,7,8,4,1] => [6,5,7,8,2,3,4,1] => 1001001
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => [5,6,7,8,2,3,4,1] => 0001001
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => [8,4,7,3,6,2,5,1] => 1010101
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [4,3,2,7,8,6,5,1] => [4,7,8,3,6,2,5,1] => 0010101
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [4,3,2,6,8,7,5,1] => [4,8,3,6,7,2,5,1] => 0100101
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => [8,7,3,4,6,2,5,1] => 1100101
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [3,4,2,6,7,8,5,1] => [3,4,6,7,8,2,5,1] => 0000101
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => [8,7,4,6,2,3,5,1] => 1101001
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => [8,4,6,7,2,3,5,1] => 1001001
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [2,4,3,6,7,8,5,1] => [4,6,7,8,2,3,5,1] => 0001001
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [3,2,4,7,8,6,5,1] => [7,8,3,6,2,4,5,1] => 0101001
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [3,2,4,7,6,8,5,1] => [7,3,6,8,2,4,5,1] => 1001001
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => [8,7,6,2,3,4,5,1] => 1110001
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [2,3,4,7,8,6,5,1] => [7,8,6,2,3,4,5,1] => 0110001
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [2,3,4,6,8,7,5,1] => [8,6,7,2,3,4,5,1] => 1010001
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [2,3,4,7,6,8,5,1] => [7,6,8,2,3,4,5,1] => 1010001
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => [6,7,8,2,3,4,5,1] => 0010001
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => [5,4,8,3,7,2,6,1] => 1010101
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => [5,4,3,7,8,2,6,1] => 1100101
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [4,5,3,2,8,7,6,1] => [4,5,8,3,7,2,6,1] => 0010101
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [4,5,3,2,7,8,6,1] => [4,5,3,7,8,2,6,1] => 0100101
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [4,3,5,2,8,7,6,1] => [4,8,3,5,7,2,6,1] => 0100101
[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [3,4,5,2,7,8,6,1] => [3,4,5,7,8,2,6,1] => 0000101
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => [5,8,4,7,2,3,6,1] => 0101001
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => [5,4,7,8,2,3,6,1] => 1001001
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [3,2,5,4,7,8,6,1] => [3,5,7,8,2,4,6,1] => 0001001
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => [4,8,3,7,2,5,6,1] => 0101001
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [3,4,2,5,8,7,6,1] => [8,3,4,7,2,5,6,1] => 1001001
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [3,4,2,5,7,8,6,1] => [3,4,7,8,2,5,6,1] => 0001001
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [3,2,4,5,7,8,6,1] => [3,7,8,2,4,5,6,1] => 0010001
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => [8,7,2,3,4,5,6,1] => 1100001
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => [7,8,2,3,4,5,6,1] => 0100001
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => [6,5,4,3,8,2,7,1] => 1110101
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [5,6,4,3,2,8,7,1] => [5,6,4,3,8,2,7,1] => 0110101
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [4,6,5,3,2,8,7,1] => [6,4,5,3,8,2,7,1] => 1010101
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => [5,4,6,3,8,2,7,1] => 1010101
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [4,5,6,3,2,8,7,1] => [4,5,6,3,8,2,7,1] => 0010101
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [3,6,5,4,2,8,7,1] => [6,5,3,4,8,2,7,1] => 1100101
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [3,5,6,4,2,8,7,1] => [5,6,3,4,8,2,7,1] => 0100101
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => [4,6,3,5,8,2,7,1] => 0100101
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [5,4,3,6,2,8,7,1] => [5,4,3,6,8,2,7,1] => 1100101
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => [4,5,3,6,8,2,7,1] => 0100101
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [3,5,4,6,2,8,7,1] => [5,3,4,6,8,2,7,1] => 1000101
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [3,4,5,6,2,8,7,1] => [3,4,5,6,8,2,7,1] => 0000101
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [2,4,6,5,3,8,7,1] => [6,4,5,8,2,3,7,1] => 1001001
[.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [2,4,5,6,3,8,7,1] => [4,5,6,8,2,3,7,1] => 0001001
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => [6,3,5,8,2,4,7,1] => 1001001
[.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [2,3,5,6,4,8,7,1] => [5,6,8,2,3,4,7,1] => 0010001
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [3,4,2,6,5,8,7,1] => [3,4,6,8,2,5,7,1] => 0001001
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => [4,6,8,2,3,5,7,1] => 0010001
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [3,2,4,6,5,8,7,1] => [3,6,8,2,4,5,7,1] => 0010001
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => [5,4,3,8,2,6,7,1] => 1101001
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [3,5,4,2,6,8,7,1] => [5,3,4,8,2,6,7,1] => 1001001
[.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [3,4,5,2,6,8,7,1] => [3,4,5,8,2,6,7,1] => 0001001
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => [5,4,8,2,3,6,7,1] => 1010001
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [2,4,5,3,6,8,7,1] => [4,5,8,2,3,6,7,1] => 0010001
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [3,2,5,4,6,8,7,1] => [3,5,8,2,4,6,7,1] => 0010001
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [4,3,2,5,6,8,7,1] => [4,3,8,2,5,6,7,1] => 1010001
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [3,4,2,5,6,8,7,1] => [3,4,8,2,5,6,7,1] => 0010001
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => [4,8,2,3,5,6,7,1] => 0100001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [3,2,4,5,6,8,7,1] => [3,8,2,4,5,6,7,1] => 0100001
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => [8,2,3,4,5,6,7,1] => 1000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => 1111101
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,8,1] => 0111101
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => [7,5,6,4,3,2,8,1] => 1011101
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,8,1] => 1011101
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => [5,6,7,4,3,2,8,1] => 0011101
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => [7,6,4,5,3,2,8,1] => 1101101
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [4,6,7,5,3,2,8,1] => [6,7,4,5,3,2,8,1] => 0101101
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [4,5,7,6,3,2,8,1] => [7,4,5,6,3,2,8,1] => 1001101
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => [6,5,4,7,3,2,8,1] => 1101101
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => [6,4,5,7,3,2,8,1] => 1001101
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [4,5,6,7,3,2,8,1] => 0001101
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [3,7,6,5,4,2,8,1] => [7,6,5,3,4,2,8,1] => 1110101
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [3,5,7,6,4,2,8,1] => [7,5,6,3,4,2,8,1] => 1010101
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [3,6,5,7,4,2,8,1] => [6,5,7,3,4,2,8,1] => 1010101
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [3,5,6,7,4,2,8,1] => [5,6,7,3,4,2,8,1] => 0010101
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [4,3,7,6,5,2,8,1] => [7,4,6,3,5,2,8,1] => 1010101
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [3,4,7,6,5,2,8,1] => [7,6,3,4,5,2,8,1] => 1100101
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [5,4,3,7,6,2,8,1] => [5,4,7,3,6,2,8,1] => 1010101
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [4,5,3,7,6,2,8,1] => [4,5,7,3,6,2,8,1] => 0010101
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => [5,7,3,4,6,2,8,1] => 0100101
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [4,3,5,7,6,2,8,1] => [4,7,3,5,6,2,8,1] => 0100101
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => [7,3,4,5,6,2,8,1] => 1000101
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,8,1] => 1110101
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => [6,4,5,3,7,2,8,1] => 1010101
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,8,1] => 1010101
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [4,5,6,3,7,2,8,1] => 0010101
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => [6,5,3,4,7,2,8,1] => 1100101
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => [5,6,3,4,7,2,8,1] => 0100101
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [4,6,3,5,7,2,8,1] => 0100101
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [3,4,6,5,7,2,8,1] => [6,3,4,5,7,2,8,1] => 1000101
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => [5,4,3,6,7,2,8,1] => 1100101
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [4,5,3,6,7,2,8,1] => 0100101
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [4,3,5,6,7,2,8,1] => [4,3,5,6,7,2,8,1] => 1000101
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [3,4,5,6,7,2,8,1] => 0000101
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => [7,6,5,4,2,3,8,1] => 1111001
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [2,5,7,6,4,3,8,1] => [7,5,6,4,2,3,8,1] => 1011001
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [2,6,5,7,4,3,8,1] => [6,5,7,4,2,3,8,1] => 1011001
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [2,5,6,7,4,3,8,1] => [5,6,7,4,2,3,8,1] => 0011001
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [2,4,7,6,5,3,8,1] => [7,6,4,5,2,3,8,1] => 1101001
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => [6,7,4,5,2,3,8,1] => 0101001
[.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [2,4,5,7,6,3,8,1] => [7,4,5,6,2,3,8,1] => 1001001
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [2,5,6,4,7,3,8,1] => [5,6,4,7,2,3,8,1] => 0101001
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => [6,4,5,7,2,3,8,1] => 1001001
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => [5,4,6,7,2,3,8,1] => 1001001
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => [4,5,6,7,2,3,8,1] => 0001001
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [3,2,7,6,5,4,8,1] => [7,6,3,5,2,4,8,1] => 1101001
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [3,2,6,7,5,4,8,1] => [6,7,3,5,2,4,8,1] => 0101001
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [6,3,5,7,2,4,8,1] => 1001001
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [3,2,5,6,7,4,8,1] => [3,5,6,7,2,4,8,1] => 0001001
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => [7,6,5,2,3,4,8,1] => 1110001
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [2,3,5,7,6,4,8,1] => [7,5,6,2,3,4,8,1] => 1010001
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => [5,6,7,2,3,4,8,1] => 0010001
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => [4,7,3,6,2,5,8,1] => 0101001
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => [3,4,6,7,2,5,8,1] => 0001001
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [2,4,3,7,6,5,8,1] => [7,4,6,2,3,5,8,1] => 1010001
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [2,4,3,6,7,5,8,1] => [4,6,7,2,3,5,8,1] => 0010001
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1] => [7,3,6,2,4,5,8,1] => 1010001
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [3,2,4,6,7,5,8,1] => [3,6,7,2,4,5,8,1] => 0010001
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => [7,6,2,3,4,5,8,1] => 1100001
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => [6,7,2,3,4,5,8,1] => 0100001
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [4,3,5,7,2,6,8,1] => 1001001
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [3,4,5,2,7,6,8,1] => [3,4,5,7,2,6,8,1] => 0001001
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => [5,4,7,2,3,6,8,1] => 1010001
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [2,4,5,3,7,6,8,1] => [4,5,7,2,3,6,8,1] => 0010001
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [3,5,7,2,4,6,8,1] => 0010001
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => [5,7,2,3,4,6,8,1] => 0100001
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1] => [4,3,7,2,5,6,8,1] => 1010001
[.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [3,4,2,5,7,6,8,1] => [3,4,7,2,5,6,8,1] => 0010001
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => [7,2,3,4,5,6,8,1] => 1000001
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [6,5,4,3,2,7,8,1] => 1111001
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => [5,4,6,3,2,7,8,1] => 1011001
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => [4,5,6,3,2,7,8,1] => 0011001
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [3,6,5,4,2,7,8,1] => [6,5,3,4,2,7,8,1] => 1101001
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => [6,3,4,5,2,7,8,1] => 1001001
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [5,4,3,6,2,7,8,1] => 1101001
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => [4,3,5,6,2,7,8,1] => 1001001
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => [3,4,5,6,2,7,8,1] => 0001001
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [2,6,5,4,3,7,8,1] => [6,5,4,2,3,7,8,1] => 1110001
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [2,5,6,4,3,7,8,1] => [5,6,4,2,3,7,8,1] => 0110001
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [2,4,6,5,3,7,8,1] => [6,4,5,2,3,7,8,1] => 1010001
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [2,5,4,6,3,7,8,1] => [5,4,6,2,3,7,8,1] => 1010001
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [2,4,5,6,3,7,8,1] => [4,5,6,2,3,7,8,1] => 0010001
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [3,2,5,6,4,7,8,1] => [3,5,6,2,4,7,8,1] => 0010001
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => [6,5,2,3,4,7,8,1] => 1100001
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [4,3,2,6,5,7,8,1] => [4,3,6,2,5,7,8,1] => 1010001
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => [6,2,3,4,5,7,8,1] => 1000001
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,8,1] => 1110001
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => [4,5,3,2,6,7,8,1] => 0110001
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [3,5,4,2,6,7,8,1] => [5,3,4,2,6,7,8,1] => 1010001
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => [4,3,5,2,6,7,8,1] => 1010001
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,8,1] => 0010001
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => [5,4,2,3,6,7,8,1] => 1100001
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => [4,5,2,3,6,7,8,1] => 0100001
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [3,2,5,4,6,7,8,1] => [3,5,2,4,6,7,8,1] => 0100001
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => [5,2,3,4,6,7,8,1] => 1000001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,8,1] => 1100001
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,8,1] => 0100001
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => [4,2,3,5,6,7,8,1] => 1000001
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => 1000001
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => 0000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,1,2] => 1111110
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [7,8,6,5,4,3,1,2] => 0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => [8,6,7,5,4,3,1,2] => 1011110
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => [7,6,8,5,4,3,1,2] => 1011110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => [6,7,8,5,4,3,1,2] => 0011110
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => [8,7,5,6,4,3,1,2] => 1101110
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,5,7,8,6,4,3,2] => [7,8,5,6,4,3,1,2] => 0101110
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => [7,6,5,8,4,3,1,2] => 1101110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => [6,7,5,8,4,3,1,2] => 0101110
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => [7,5,6,8,4,3,1,2] => 1001110
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => [6,5,7,8,4,3,1,2] => 1001110
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => [5,6,7,8,4,3,1,2] => 0001110
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => [8,7,6,4,5,3,1,2] => 1110110
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => [7,8,6,4,5,3,1,2] => 0110110
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => [8,6,7,4,5,3,1,2] => 1010110
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => [6,7,8,4,5,3,1,2] => 0010110
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => [7,6,5,4,8,3,1,2] => 1110110
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,6,5,7,4,8,3,2] => [6,5,7,4,8,3,1,2] => 1010110
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => [7,6,4,5,8,3,1,2] => 1100110
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => [6,7,4,5,8,3,1,2] => 0100110
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => [6,5,4,7,8,3,1,2] => 1100110
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,5,6,4,7,8,3,2] => [5,6,4,7,8,3,1,2] => 0100110
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => [5,4,6,7,8,3,1,2] => 1000110
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => [4,5,6,7,8,3,1,2] => 0000110
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => [8,7,6,5,3,4,1,2] => 1111010
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,3,7,8,6,5,4,2] => [7,8,6,5,3,4,1,2] => 0111010
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,3,7,6,8,5,4,2] => [7,6,8,5,3,4,1,2] => 1011010
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => [6,7,8,5,3,4,1,2] => 0011010
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => [8,7,5,6,3,4,1,2] => 1101010
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => [7,8,5,6,3,4,1,2] => 0101010
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,3,6,5,8,7,4,2] => [6,8,5,7,3,4,1,2] => 0101010
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => [8,5,6,7,3,4,1,2] => 1001010
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,3,7,6,5,8,4,2] => [7,6,5,8,3,4,1,2] => 1101010
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,3,6,7,5,8,4,2] => [6,7,5,8,3,4,1,2] => 0101010
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,3,5,7,6,8,4,2] => [7,5,6,8,3,4,1,2] => 1001010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => [6,5,7,8,3,4,1,2] => 1001010
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => [5,6,7,8,3,4,1,2] => 0001010
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => [8,7,4,6,3,5,1,2] => 1101010
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => [7,8,4,6,3,5,1,2] => 0101010
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => [7,4,6,8,3,5,1,2] => 1001010
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,4,3,6,7,8,5,2] => [4,6,7,8,3,5,1,2] => 0001010
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => [8,7,6,3,4,5,1,2] => 1110010
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,3,4,6,8,7,5,2] => [8,6,7,3,4,5,1,2] => 1010010
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,5,4,3,8,7,6,2] => [5,8,4,7,3,6,1,2] => 0101010
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,5,4,3,7,8,6,2] => [5,4,7,8,3,6,1,2] => 1001010
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,4,5,3,8,7,6,2] => [8,4,5,7,3,6,1,2] => 1001010
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => [5,7,8,3,4,6,1,2] => 0010010
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => [4,7,8,3,5,6,1,2] => 0010010
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => [8,7,3,4,5,6,1,2] => 1100010
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => [7,8,3,4,5,6,1,2] => 0100010
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => [6,5,4,8,3,7,1,2] => 1101010
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => [5,6,4,8,3,7,1,2] => 0101010
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,4,6,5,3,8,7,2] => [6,4,5,8,3,7,1,2] => 1001010
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => [4,6,8,3,5,7,1,2] => 0010010
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,3,4,6,5,8,7,2] => [6,8,3,4,5,7,1,2] => 0100010
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,5,4,3,6,8,7,2] => [5,4,8,3,6,7,1,2] => 1010010
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => [4,5,8,3,6,7,1,2] => 0010010
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,4,3,5,6,8,7,2] => [4,8,3,5,6,7,1,2] => 0100010
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => [8,3,4,5,6,7,1,2] => 1000010
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => [7,6,5,4,3,8,1,2] => 1111010
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,5,7,6,4,3,8,2] => [7,5,6,4,3,8,1,2] => 1011010
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => [6,5,7,4,3,8,1,2] => 1011010
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,5,6,7,4,3,8,2] => [5,6,7,4,3,8,1,2] => 0011010
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => [6,7,4,5,3,8,1,2] => 0101010
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,5,4,7,6,3,8,2] => [5,7,4,6,3,8,1,2] => 0101010
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => [5,6,4,7,3,8,1,2] => 0101010
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => [5,4,6,7,3,8,1,2] => 1001010
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => [4,5,6,7,3,8,1,2] => 0001010
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,3,5,7,6,4,8,2] => [7,5,6,3,4,8,1,2] => 1010010
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => [5,6,7,3,4,8,1,2] => 0010010
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,4,3,6,7,5,8,2] => [4,6,7,3,5,8,1,2] => 0010010
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => [7,6,3,4,5,8,1,2] => 1100010
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,5,4,3,7,6,8,2] => [5,4,7,3,6,8,1,2] => 1010010
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => [5,7,3,4,6,8,1,2] => 0100010
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => [7,3,4,5,6,8,1,2] => 1000010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,6,5,4,3,7,8,2] => [6,5,4,3,7,8,1,2] => 1110010
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,5,4,6,3,7,8,2] => [5,4,6,3,7,8,1,2] => 1010010
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,4,5,6,3,7,8,2] => [4,5,6,3,7,8,1,2] => 0010010
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,3,5,6,4,7,8,2] => [5,6,3,4,7,8,1,2] => 0100010
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => [4,6,3,5,7,8,1,2] => 0100010
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => [6,3,4,5,7,8,1,2] => 1000010
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => [5,4,3,6,7,8,1,2] => 1100010
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => [4,5,3,6,7,8,1,2] => 0100010
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,3,5,4,6,7,8,2] => [5,3,4,6,7,8,1,2] => 1000010
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [4,3,5,6,7,8,1,2] => 1000010
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => [3,4,5,6,7,8,1,2] => 0000010
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [8,7,6,5,2,4,1,3] => 1111010
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => [7,6,8,5,2,4,1,3] => 1011010
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [6,7,8,5,2,4,1,3] => 0011010
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [2,1,5,8,7,6,4,3] => [8,7,5,6,2,4,1,3] => 1101010
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [7,8,5,6,2,4,1,3] => 0101010
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => [6,8,5,7,2,4,1,3] => 0101010
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => [7,6,5,8,2,4,1,3] => 1101010
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => [6,7,5,8,2,4,1,3] => 0101010
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => [7,5,6,8,2,4,1,3] => 1001010
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => [6,5,7,8,2,4,1,3] => 1001010
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => [5,6,7,8,2,4,1,3] => 0001010
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => [8,7,6,2,4,5,1,3] => 1110010
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => [8,6,7,2,4,5,1,3] => 1010010
[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => [6,7,8,2,4,5,1,3] => 0010010
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => [7,8,2,4,5,6,1,3] => 0100010
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => [6,8,2,4,5,7,1,3] => 0100010
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => [5,8,2,4,6,7,1,3] => 0100010
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => [7,6,5,2,4,8,1,3] => 1110010
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [6,5,7,2,4,8,1,3] => 1010010
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => [7,6,2,4,5,8,1,3] => 1100010
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [5,7,2,4,6,8,1,3] => 0100010
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [2,1,4,5,7,6,8,3] => [7,2,4,5,6,8,1,3] => 1000010
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [2,1,6,5,4,7,8,3] => [6,5,2,4,7,8,1,3] => 1100010
[[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => [5,6,2,4,7,8,1,3] => 0100010
[[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [2,1,4,6,5,7,8,3] => [6,2,4,5,7,8,1,3] => 1000010
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => [2,4,5,6,7,8,1,3] => 0000010
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => [8,7,6,5,4,1,2,3] => 1111100
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => [7,8,6,5,4,1,2,3] => 0111100
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,2,7,6,8,5,4,3] => [7,6,8,5,4,1,2,3] => 1011100
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => [6,7,8,5,4,1,2,3] => 0011100
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,2,5,7,8,6,4,3] => [7,8,5,6,4,1,2,3] => 0101100
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,2,6,5,8,7,4,3] => [6,8,5,7,4,1,2,3] => 0101100
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,2,5,6,8,7,4,3] => [8,5,6,7,4,1,2,3] => 1001100
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => [7,6,5,8,4,1,2,3] => 1101100
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,2,6,7,5,8,4,3] => [6,7,5,8,4,1,2,3] => 0101100
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,2,5,7,6,8,4,3] => [7,5,6,8,4,1,2,3] => 1001100
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,2,6,5,7,8,4,3] => [6,5,7,8,4,1,2,3] => 1001100
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => [5,6,7,8,4,1,2,3] => 0001100
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [8,7,6,4,5,1,2,3] => 1110100
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => [8,6,7,4,5,1,2,3] => 1010100
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => [6,7,8,4,5,1,2,3] => 0010100
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => [8,7,4,5,6,1,2,3] => 1100100
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,2,4,5,7,8,6,3] => [7,8,4,5,6,1,2,3] => 0100100
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => [6,8,4,5,7,1,2,3] => 0100100
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => [8,4,5,6,7,1,2,3] => 1000100
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => [7,6,5,4,8,1,2,3] => 1110100
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,2,6,7,5,4,8,3] => [6,7,5,4,8,1,2,3] => 0110100
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,2,5,7,6,4,8,3] => [7,5,6,4,8,1,2,3] => 1010100
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,2,6,5,7,4,8,3] => [6,5,7,4,8,1,2,3] => 1010100
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => [5,6,7,4,8,1,2,3] => 0010100
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => [7,6,4,5,8,1,2,3] => 1100100
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,2,4,6,7,5,8,3] => [6,7,4,5,8,1,2,3] => 0100100
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,2,5,4,7,6,8,3] => [5,7,4,6,8,1,2,3] => 0100100
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => [6,5,4,7,8,1,2,3] => 1100100
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => [5,6,4,7,8,1,2,3] => 0100100
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,2,4,6,5,7,8,3] => [6,4,5,7,8,1,2,3] => 1000100
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [5,4,6,7,8,1,2,3] => 1000100
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => [4,5,6,7,8,1,2,3] => 0000100
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => [8,7,3,6,2,5,1,4] => 1101010
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => [7,8,3,6,2,5,1,4] => 0101010
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => [8,3,7,2,5,6,1,4] => 1010010
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => [3,7,8,2,5,6,1,4] => 0010010
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => [3,6,8,2,5,7,1,4] => 0010010
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => [3,8,2,5,6,7,1,4] => 0100010
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => [3,6,7,2,5,8,1,4] => 0010010
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => [3,6,2,5,7,8,1,4] => 0100010
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => [3,2,5,6,7,8,1,4] => 1000010
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [2,3,1,7,8,6,5,4] => [7,8,6,2,3,5,1,4] => 0110010
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => [7,6,8,2,3,5,1,4] => 1010010
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [2,3,1,5,7,8,6,4] => [7,8,2,3,5,6,1,4] => 0100010
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => [6,8,2,3,5,7,1,4] => 0100010
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [2,3,1,5,6,8,7,4] => [8,2,3,5,6,7,1,4] => 1000010
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [2,3,1,7,6,5,8,4] => [7,6,2,3,5,8,1,4] => 1100010
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => [2,3,5,6,7,8,1,4] => 0000010
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => [8,7,6,3,5,1,2,4] => 1110100
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,3,2,7,8,6,5,4] => [7,8,6,3,5,1,2,4] => 0110100
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => [8,6,7,3,5,1,2,4] => 1010100
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => [7,6,8,3,5,1,2,4] => 1010100
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => [6,7,8,3,5,1,2,4] => 0010100
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,3,2,5,8,7,6,4] => [8,7,3,5,6,1,2,4] => 1100100
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => [7,8,3,5,6,1,2,4] => 0100100
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => [6,8,3,5,7,1,2,4] => 0100100
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => [8,3,5,6,7,1,2,4] => 1000100
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => [7,6,3,5,8,1,2,4] => 1100100
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => [6,7,3,5,8,1,2,4] => 0100100
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,3,2,5,7,6,8,4] => [7,3,5,6,8,1,2,4] => 1000100
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,3,2,5,6,7,8,4] => [3,5,6,7,8,1,2,4] => 0000100
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => [8,7,6,2,5,1,3,4] => 1110100
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => [7,8,6,2,5,1,3,4] => 0110100
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => [8,6,7,2,5,1,3,4] => 1010100
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [2,1,3,7,6,8,5,4] => [7,6,8,2,5,1,3,4] => 1010100
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [2,1,3,5,8,7,6,4] => [8,7,2,5,6,1,3,4] => 1100100
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [2,1,3,5,7,8,6,4] => [7,8,2,5,6,1,3,4] => 0100100
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => [6,8,2,5,7,1,3,4] => 0100100
[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [2,1,3,5,6,8,7,4] => [8,2,5,6,7,1,3,4] => 1000100
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => [7,2,5,6,8,1,3,4] => 1000100
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [2,1,3,6,5,7,8,4] => [6,2,5,7,8,1,3,4] => 1000100
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => [2,5,6,7,8,1,3,4] => 0000100
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [8,7,6,5,1,2,3,4] => 1111000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => [7,8,6,5,1,2,3,4] => 0111000
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [8,6,7,5,1,2,3,4] => 1011000
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => [7,6,8,5,1,2,3,4] => 1011000
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => [6,7,8,5,1,2,3,4] => 0011000
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => [8,7,5,6,1,2,3,4] => 1101000
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => [7,8,5,6,1,2,3,4] => 0101000
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => [6,8,5,7,1,2,3,4] => 0101000
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => [8,5,6,7,1,2,3,4] => 1001000
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => [7,6,5,8,1,2,3,4] => 1101000
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => [6,7,5,8,1,2,3,4] => 0101000
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => [7,5,6,8,1,2,3,4] => 1001000
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [6,5,7,8,1,2,3,4] => 1001000
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [5,6,7,8,1,2,3,4] => 0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [4,8,3,7,2,6,1,5] => 0101010
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => [4,3,7,8,2,6,1,5] => 1001010
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => [4,3,8,2,6,7,1,5] => 1010010
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => [4,3,7,2,6,8,1,5] => 1010010
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => [4,3,2,6,7,8,1,5] => 1100010
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => [8,3,4,7,2,6,1,5] => 1001010
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [3,4,7,8,2,6,1,5] => 0001010
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => [3,4,8,2,6,7,1,5] => 0010010
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => [3,4,7,2,6,8,1,5] => 0010010
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => [3,4,2,6,7,8,1,5] => 0100010
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => [8,4,7,2,3,6,1,5] => 1010010
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => [4,8,2,3,6,7,1,5] => 0100010
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => [4,7,2,3,6,8,1,5] => 0100010
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => [4,2,3,6,7,8,1,5] => 1000010
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [8,3,7,2,4,6,1,5] => 1010010
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => [3,7,8,2,4,6,1,5] => 0010010
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [3,8,2,4,6,7,1,5] => 0100010
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [3,7,2,4,6,8,1,5] => 0100010
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => [3,2,4,6,7,8,1,5] => 1000010
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => [8,7,2,3,4,6,1,5] => 1100010
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => [7,8,2,3,4,6,1,5] => 0100010
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => [8,2,3,4,6,7,1,5] => 1000010
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => [7,2,3,4,6,8,1,5] => 1000010
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [2,3,4,6,7,8,1,5] => 0000010
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => [8,4,7,3,6,1,2,5] => 1010100
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,4,3,2,6,8,7,5] => [4,8,3,6,7,1,2,5] => 0100100
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [4,7,3,6,8,1,2,5] => 0100100
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => [4,3,6,7,8,1,2,5] => 1000100
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => [8,7,3,4,6,1,2,5] => 1100100
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => [7,3,4,6,8,1,2,5] => 1000100
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => [3,4,6,7,8,1,2,5] => 0000100
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [8,7,2,4,6,1,3,5] => 1100100
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [7,8,2,4,6,1,3,5] => 0100100
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [8,2,4,6,7,1,3,5] => 1000100
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [7,2,4,6,8,1,3,5] => 1000100
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => [2,4,6,7,8,1,3,5] => 0000100
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => [8,7,4,6,1,2,3,5] => 1101000
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,2,4,3,7,8,6,5] => [7,8,4,6,1,2,3,5] => 0101000
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => [8,4,6,7,1,2,3,5] => 1001000
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => [7,4,6,8,1,2,3,5] => 1001000
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => [4,6,7,8,1,2,3,5] => 0001000
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => [8,3,7,2,6,1,4,5] => 1010100
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => [3,7,8,2,6,1,4,5] => 0010100
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => [3,8,2,6,7,1,4,5] => 0100100
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => [3,7,2,6,8,1,4,5] => 0100100
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => [3,2,6,7,8,1,4,5] => 1000100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => [8,7,2,3,6,1,4,5] => 1100100
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [2,3,1,4,7,8,6,5] => [7,8,2,3,6,1,4,5] => 0100100
[[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [2,3,1,4,6,8,7,5] => [8,2,3,6,7,1,4,5] => 1000100
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => [7,2,3,6,8,1,4,5] => 1000100
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => [2,3,6,7,8,1,4,5] => 0000100
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => [8,7,3,6,1,2,4,5] => 1101000
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => [3,6,7,8,1,2,4,5] => 0001000
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => [8,7,2,6,1,3,4,5] => 1101000
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [2,1,3,4,6,8,7,5] => [8,2,6,7,1,3,4,5] => 1001000
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => [2,6,7,8,1,3,4,5] => 0001000
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => [8,7,6,1,2,3,4,5] => 1110000
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => [7,8,6,1,2,3,4,5] => 0110000
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => [8,6,7,1,2,3,4,5] => 1010000
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [7,6,8,1,2,3,4,5] => 1010000
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => [6,7,8,1,2,3,4,5] => 0010000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => [5,4,3,8,2,7,1,6] => 1101010
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => [5,4,3,2,7,8,1,6] => 1110010
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => [4,5,3,8,2,7,1,6] => 0101010
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [4,5,3,2,1,7,8,6] => [4,5,3,2,7,8,1,6] => 0110010
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => [3,4,5,8,2,7,1,6] => 0001010
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [3,4,5,2,1,7,8,6] => [3,4,5,2,7,8,1,6] => 0010010
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => [4,5,8,2,3,7,1,6] => 0010010
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => [3,5,8,2,4,7,1,6] => 0010010
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => [5,8,2,3,4,7,1,6] => 0100010
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => [4,3,8,2,5,7,1,6] => 1010010
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => [4,3,2,5,7,8,1,6] => 1100010
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => [4,8,2,3,5,7,1,6] => 0100010
[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [3,2,4,5,1,7,8,6] => [3,2,4,5,7,8,1,6] => 1000010
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => [8,2,3,4,5,7,1,6] => 1000010
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => [2,3,4,5,7,8,1,6] => 0000010
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => [5,4,8,3,7,1,2,6] => 1010100
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,5,4,3,2,7,8,6] => [5,4,3,7,8,1,2,6] => 1100100
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => [4,5,8,3,7,1,2,6] => 0010100
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,4,5,3,2,7,8,6] => [4,5,3,7,8,1,2,6] => 0100100
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => [5,3,4,7,8,1,2,6] => 1000100
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,4,3,5,2,8,7,6] => [4,8,3,5,7,1,2,6] => 0100100
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => [8,3,4,5,7,1,2,6] => 1000100
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => [3,4,5,7,8,1,2,6] => 0000100
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => [5,8,2,4,7,1,3,6] => 0100100
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [2,1,5,4,3,7,8,6] => [5,2,4,7,8,1,3,6] => 1000100
[[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [2,1,4,5,3,7,8,6] => [2,4,5,7,8,1,3,6] => 0000100
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => [5,8,4,7,1,2,3,6] => 0101000
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => [4,5,7,8,1,2,3,6] => 0001000
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [3,2,1,5,4,8,7,6] => [3,8,2,5,7,1,4,6] => 0100100
[[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [2,3,1,5,4,7,8,6] => [2,3,5,7,8,1,4,6] => 0000100
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => [8,3,5,7,1,2,4,6] => 1001000
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => [3,5,7,8,1,2,4,6] => 0001000
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => [8,2,5,7,1,3,4,6] => 1001000
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [2,1,3,5,4,7,8,6] => [2,5,7,8,1,3,4,6] => 0001000
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => [8,5,7,1,2,3,4,6] => 1010000
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => [5,7,8,1,2,3,4,6] => 0010000
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => [4,3,8,2,7,1,5,6] => 1010100
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => [4,3,2,7,8,1,5,6] => 1100100
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [3,4,2,1,5,8,7,6] => [3,4,8,2,7,1,5,6] => 0010100
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [3,4,2,1,5,7,8,6] => [3,4,2,7,8,1,5,6] => 0100100
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [3,8,2,4,7,1,5,6] => 0100100
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => [3,2,4,7,8,1,5,6] => 1000100
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => [8,2,3,4,7,1,5,6] => 1000100
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => [2,3,4,7,8,1,5,6] => 0000100
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => [4,8,3,7,1,2,5,6] => 0101000
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,4,3,2,5,7,8,6] => [4,3,7,8,1,2,5,6] => 1001000
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => [3,4,7,8,1,2,5,6] => 0001000
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => [8,2,4,7,1,3,5,6] => 1001000
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => [2,4,7,8,1,3,5,6] => 0001000
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => [8,4,7,1,2,3,5,6] => 1010000
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => [4,7,8,1,2,3,5,6] => 0010000
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [3,8,2,7,1,4,5,6] => 0101000
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [3,2,1,4,5,7,8,6] => [3,2,7,8,1,4,5,6] => 1001000
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [2,3,1,4,5,8,7,6] => [8,2,3,7,1,4,5,6] => 1001000
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [2,3,7,8,1,4,5,6] => 0001000
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => [8,3,7,1,2,4,5,6] => 1010000
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => [3,7,8,1,2,4,5,6] => 0010000
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => [2,7,8,1,3,4,5,6] => 0010000
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [8,7,1,2,3,4,5,6] => 1100000
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [7,8,1,2,3,4,5,6] => 0100000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,8,1,7] => 1111010
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => [5,6,4,3,2,8,1,7] => 0111010
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => [6,4,5,3,2,8,1,7] => 1011010
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [4,5,6,3,2,8,1,7] => 0011010
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => [6,5,3,4,2,8,1,7] => 1101010
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => [5,6,3,4,2,8,1,7] => 0101010
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => [4,6,3,5,2,8,1,7] => 0101010
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => [4,5,3,6,2,8,1,7] => 0101010
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [3,5,4,6,2,1,8,7] => [5,3,4,6,2,8,1,7] => 1001010
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => [4,3,5,6,2,8,1,7] => 1001010
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => [3,4,5,6,2,8,1,7] => 0001010
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [2,5,6,4,3,1,8,7] => [5,6,4,2,3,8,1,7] => 0110010
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => [6,4,5,2,3,8,1,7] => 1010010
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [2,5,4,6,3,1,8,7] => [5,4,6,2,3,8,1,7] => 1010010
[[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [2,4,5,6,3,1,8,7] => [4,5,6,2,3,8,1,7] => 0010010
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => [6,3,5,2,4,8,1,7] => 1010010
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [3,2,5,6,4,1,8,7] => [3,5,6,2,4,8,1,7] => 0010010
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => [6,5,2,3,4,8,1,7] => 1100010
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => [4,6,2,3,5,8,1,7] => 0100010
[[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [2,3,4,6,5,1,8,7] => [6,2,3,4,5,8,1,7] => 1000010
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => [5,4,3,2,6,8,1,7] => 1110010
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [4,3,5,2,6,8,1,7] => 1010010
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [2,5,4,3,6,1,8,7] => [5,4,2,3,6,8,1,7] => 1100010
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [3,5,2,4,6,8,1,7] => 0100010
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => [4,3,2,5,6,8,1,7] => 1100010
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [3,4,2,5,6,1,8,7] => [3,4,2,5,6,8,1,7] => 0100010
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [2,4,3,5,6,1,8,7] => [4,2,3,5,6,8,1,7] => 1000010
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => [2,3,4,5,6,8,1,7] => 0000010
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => [6,5,4,3,8,1,2,7] => 1110100
[[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,4,5,6,3,2,8,7] => [4,5,6,3,8,1,2,7] => 0010100
[[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,3,4,6,5,2,8,7] => [6,3,4,5,8,1,2,7] => 1000100
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => [3,4,5,6,8,1,2,7] => 0000100
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [6,5,2,4,8,1,3,7] => 1100100
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [5,6,2,4,8,1,3,7] => 0100100
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => [6,2,4,5,8,1,3,7] => 1000100
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [5,2,4,6,8,1,3,7] => 1000100
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [2,4,5,6,8,1,3,7] => 0000100
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,2,6,5,4,3,8,7] => [6,5,4,8,1,2,3,7] => 1101000
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,2,4,6,5,3,8,7] => [6,4,5,8,1,2,3,7] => 1001000
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => [4,5,6,8,1,2,3,7] => 0001000
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => [3,6,2,5,8,1,4,7] => 0100100
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [3,2,1,5,6,4,8,7] => [3,2,5,6,8,1,4,7] => 1000100
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => [6,2,3,5,8,1,4,7] => 1000100
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [2,3,1,5,6,4,8,7] => [2,3,5,6,8,1,4,7] => 0000100
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => [6,3,5,8,1,2,4,7] => 1001000
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,3,2,5,6,4,8,7] => [3,5,6,8,1,2,4,7] => 0001000
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => [6,2,5,8,1,3,4,7] => 1001000
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => [2,5,6,8,1,3,4,7] => 0001000
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => [6,5,8,1,2,3,4,7] => 1010000
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => [5,6,8,1,2,3,4,7] => 0010000
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [4,3,2,6,8,1,5,7] => 1100100
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [3,4,2,6,8,1,5,7] => 0100100
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => [4,2,3,6,8,1,5,7] => 1000100
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [3,2,4,6,8,1,5,7] => 1000100
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => [2,3,4,6,8,1,5,7] => 0000100
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,4,3,2,6,5,8,7] => [4,3,6,8,1,2,5,7] => 1001000
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => [3,4,6,8,1,2,5,7] => 0001000
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,4,6,8,1,3,5,7] => 0001000
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => [4,6,8,1,2,3,5,7] => 0010000
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [3,2,1,4,6,5,8,7] => [3,2,6,8,1,4,5,7] => 1001000
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [2,3,1,4,6,5,8,7] => [2,3,6,8,1,4,5,7] => 0001000
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,3,2,4,6,5,8,7] => [3,6,8,1,2,4,5,7] => 0010000
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => [2,6,8,1,3,4,5,7] => 0010000
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => [6,8,1,2,3,4,5,7] => 0100000
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => [5,4,3,2,8,1,6,7] => 1110100
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [4,3,5,2,1,6,8,7] => [4,3,5,2,8,1,6,7] => 1010100
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [2,5,4,3,1,6,8,7] => [5,4,2,3,8,1,6,7] => 1100100
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [3,2,5,4,1,6,8,7] => [3,5,2,4,8,1,6,7] => 0100100
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [2,3,5,4,1,6,8,7] => [5,2,3,4,8,1,6,7] => 1000100
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [4,3,2,5,1,6,8,7] => [4,3,2,5,8,1,6,7] => 1100100
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => [4,2,3,5,8,1,6,7] => 1000100
[[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [3,2,4,5,1,6,8,7] => [3,2,4,5,8,1,6,7] => 1000100
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => [2,3,4,5,8,1,6,7] => 0000100
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,5,4,3,2,6,8,7] => [5,4,3,8,1,2,6,7] => 1101000
[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,4,3,5,2,6,8,7] => [4,3,5,8,1,2,6,7] => 1001000
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,3,4,5,2,6,8,7] => [3,4,5,8,1,2,6,7] => 0001000
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => [5,2,4,8,1,3,6,7] => 1001000
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => [2,4,5,8,1,3,6,7] => 0001000
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => [5,4,8,1,2,3,6,7] => 1010000
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,2,4,5,3,6,8,7] => [4,5,8,1,2,3,6,7] => 0010000
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [3,2,1,5,4,6,8,7] => [3,2,5,8,1,4,6,7] => 1001000
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => [2,5,8,1,3,4,6,7] => 0010000
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => [5,8,1,2,3,4,6,7] => 0100000
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => [4,3,2,8,1,5,6,7] => 1101000
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [3,4,2,1,5,6,8,7] => [3,4,2,8,1,5,6,7] => 0101000
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [2,4,3,1,5,6,8,7] => [4,2,3,8,1,5,6,7] => 1001000
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => [3,2,4,8,1,5,6,7] => 1001000
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => [2,3,4,8,1,5,6,7] => 0001000
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => [3,4,8,1,2,5,6,7] => 0010000
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => [2,4,8,1,3,5,6,7] => 0010000
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => [4,8,1,2,3,5,6,7] => 0100000
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => [3,2,8,1,4,5,6,7] => 1010000
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => [2,3,8,1,4,5,6,7] => 0010000
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => [3,8,1,2,4,5,6,7] => 0100000
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => 0100000
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => 1000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => 1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1,8] => 0111110
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => [7,5,6,4,3,2,1,8] => 1011110
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1,8] => 1011110
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1,8] => 0011110
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => [7,6,4,5,3,2,1,8] => 1101110
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => [6,7,4,5,3,2,1,8] => 0101110
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => [5,7,4,6,3,2,1,8] => 0101110
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => [7,4,5,6,3,2,1,8] => 1001110
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1,8] => 1101110
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => [5,6,4,7,3,2,1,8] => 0101110
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => [5,4,6,7,3,2,1,8] => 1001110
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [4,5,6,7,3,2,1,8] => 0001110
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [3,7,6,5,4,2,1,8] => [7,6,5,3,4,2,1,8] => 1110110
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [3,5,7,6,4,2,1,8] => [7,5,6,3,4,2,1,8] => 1010110
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [4,3,7,6,5,2,1,8] => [7,4,6,3,5,2,1,8] => 1010110
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => [7,6,3,4,5,2,1,8] => 1100110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [5,4,3,7,6,2,1,8] => [5,4,7,3,6,2,1,8] => 1010110
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [4,3,5,7,6,2,1,8] => [4,7,3,5,6,2,1,8] => 0100110
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [6,5,4,3,7,2,1,8] => 1110110
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [5,6,4,3,7,2,1,8] => 0110110
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [5,4,6,3,7,2,1,8] => 1010110
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [5,4,3,6,7,2,1,8] => 1100110
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => [3,4,5,6,7,2,1,8] => 0000110
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [7,6,5,4,2,3,1,8] => 1111010
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => [6,7,5,4,2,3,1,8] => 0111010
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => [7,5,6,4,2,3,1,8] => 1011010
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [2,4,7,6,5,3,1,8] => [7,6,4,5,2,3,1,8] => 1101010
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => [6,7,4,5,2,3,1,8] => 0101010
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [2,5,4,7,6,3,1,8] => [5,7,4,6,2,3,1,8] => 0101010
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [2,4,5,7,6,3,1,8] => [7,4,5,6,2,3,1,8] => 1001010
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => [5,6,4,7,2,3,1,8] => 0101010
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [2,5,4,6,7,3,1,8] => [5,4,6,7,2,3,1,8] => 1001010
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [2,4,5,6,7,3,1,8] => [4,5,6,7,2,3,1,8] => 0001010
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => [7,6,3,5,2,4,1,8] => 1101010
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => [6,7,3,5,2,4,1,8] => 0101010
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [3,2,5,6,7,4,1,8] => [3,5,6,7,2,4,1,8] => 0001010
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => [7,6,5,2,3,4,1,8] => 1110010
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [2,3,5,6,7,4,1,8] => [5,6,7,2,3,4,1,8] => 0010010
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [4,3,2,7,6,5,1,8] => [4,7,3,6,2,5,1,8] => 0101010
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [2,4,3,7,6,5,1,8] => [7,4,6,2,3,5,1,8] => 1010010
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => [7,6,2,3,4,5,1,8] => 1100010
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [2,3,4,6,7,5,1,8] => [6,7,2,3,4,5,1,8] => 0100010
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => [5,4,3,7,2,6,1,8] => 1101010
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => [4,5,3,7,2,6,1,8] => 0101010
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => [5,3,4,7,2,6,1,8] => 1001010
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [4,3,5,2,7,6,1,8] => [4,3,5,7,2,6,1,8] => 1001010
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => [3,5,7,2,4,6,1,8] => 0010010
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [4,3,2,5,7,6,1,8] => [4,3,7,2,5,6,1,8] => 1010010
[[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [2,4,3,5,7,6,1,8] => [4,7,2,3,5,6,1,8] => 0100010
[[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [3,2,4,5,7,6,1,8] => [3,7,2,4,5,6,1,8] => 0100010
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => [7,2,3,4,5,6,1,8] => 1000010
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [6,5,4,3,2,7,1,8] => 1111010
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => [5,6,4,3,2,7,1,8] => 0111010
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => [5,4,6,3,2,7,1,8] => 1011010
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [3,5,6,4,2,7,1,8] => [5,6,3,4,2,7,1,8] => 0101010
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [4,3,6,5,2,7,1,8] => [4,6,3,5,2,7,1,8] => 0101010
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => [6,3,4,5,2,7,1,8] => 1001010
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [5,4,3,6,2,7,1,8] => 1101010
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1,8] => 0101010
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => [5,3,4,6,2,7,1,8] => 1001010
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => [4,3,5,6,2,7,1,8] => 1001010
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [3,4,5,6,2,7,1,8] => 0001010
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => [5,4,6,2,3,7,1,8] => 1010010
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [4,3,2,6,5,7,1,8] => [4,3,6,2,5,7,1,8] => 1010010
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [3,4,2,6,5,7,1,8] => [3,4,6,2,5,7,1,8] => 0010010
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => [4,6,2,3,5,7,1,8] => 0100010
[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [3,2,4,6,5,7,1,8] => [3,6,2,4,5,7,1,8] => 0100010
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => [6,2,3,4,5,7,1,8] => 1000010
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1,8] => 1110010
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => [3,4,5,2,6,7,1,8] => 0010010
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => [5,4,2,3,6,7,1,8] => 1100010
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [2,4,5,3,6,7,1,8] => [4,5,2,3,6,7,1,8] => 0100010
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [2,3,5,4,6,7,1,8] => [5,2,3,4,6,7,1,8] => 1000010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => [4,3,2,5,6,7,1,8] => 1100010
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [3,4,2,5,6,7,1,8] => 0100010
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [2,4,3,5,6,7,1,8] => [4,2,3,5,6,7,1,8] => 1000010
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1,8] => 1000010
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => 0000010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => [7,6,5,4,3,1,2,8] => 1111100
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [6,7,5,4,3,1,2,8] => 0111100
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,5,7,6,4,3,2,8] => [7,5,6,4,3,1,2,8] => 1011100
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,4,7,6,5,3,2,8] => [7,6,4,5,3,1,2,8] => 1101100
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,4,5,7,6,3,2,8] => [7,4,5,6,3,1,2,8] => 1001100
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => [5,4,6,7,3,1,2,8] => 1001100
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => [4,5,6,7,3,1,2,8] => 0001100
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,3,7,6,5,4,2,8] => [7,6,5,3,4,1,2,8] => 1110100
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => [7,5,6,3,4,1,2,8] => 1010100
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => [6,7,3,4,5,1,2,8] => 0100100
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => [5,7,3,4,6,1,2,8] => 0100100
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => [4,7,3,5,6,1,2,8] => 0100100
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,6,5,4,3,7,2,8] => [6,5,4,3,7,1,2,8] => 1110100
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => [5,6,3,4,7,1,2,8] => 0100100
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => [4,6,3,5,7,1,2,8] => 0100100
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,3,4,6,5,7,2,8] => [6,3,4,5,7,1,2,8] => 1000100
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,4,3,5,6,7,2,8] => [4,3,5,6,7,1,2,8] => 1000100
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => [3,4,5,6,7,1,2,8] => 0000100
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [2,1,5,4,6,7,3,8] => [5,2,4,6,7,1,3,8] => 1000100
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [2,1,4,5,6,7,3,8] => [2,4,5,6,7,1,3,8] => 0000100
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => [7,6,5,4,1,2,3,8] => 1111000
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,2,5,7,6,4,3,8] => [7,5,6,4,1,2,3,8] => 1011000
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => [5,6,7,4,1,2,3,8] => 0011000
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,2,4,7,6,5,3,8] => [7,6,4,5,1,2,3,8] => 1101000
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,2,4,5,7,6,3,8] => [7,4,5,6,1,2,3,8] => 1001000
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => [4,5,6,7,1,2,3,8] => 0001000
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => [7,3,6,2,5,1,4,8] => 1010100
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [3,2,1,6,5,7,4,8] => [3,6,2,5,7,1,4,8] => 0100100
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [2,3,1,7,6,5,4,8] => [7,6,2,3,5,1,4,8] => 1100100
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [2,3,1,6,5,7,4,8] => [6,2,3,5,7,1,4,8] => 1000100
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => [2,3,5,6,7,1,4,8] => 0000100
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => [7,6,3,5,1,2,4,8] => 1101000
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => [7,3,5,6,1,2,4,8] => 1001000
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => [6,3,5,7,1,2,4,8] => 1001000
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,3,2,5,6,7,4,8] => [3,5,6,7,1,2,4,8] => 0001000
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [2,1,3,6,7,5,4,8] => [6,7,2,5,1,3,4,8] => 0101000
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => [7,6,5,1,2,3,4,8] => 1110000
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => [6,7,5,1,2,3,4,8] => 0110000
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => [7,5,6,1,2,3,4,8] => 1010000
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => [6,5,7,1,2,3,4,8] => 1010000
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => [5,6,7,1,2,3,4,8] => 0010000
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => [4,3,7,2,6,1,5,8] => 1010100
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => [4,3,2,6,7,1,5,8] => 1100100
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => [2,3,4,6,7,1,5,8] => 0000100
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [4,7,3,6,1,2,5,8] => 0101000
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,3,4,2,7,6,5,8] => [7,3,4,6,1,2,5,8] => 1001000
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [3,4,6,7,1,2,5,8] => 0001000
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [2,1,4,3,7,6,5,8] => [7,2,4,6,1,3,5,8] => 1001000
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [2,1,4,3,6,7,5,8] => [2,4,6,7,1,3,5,8] => 0001000
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,2,4,3,7,6,5,8] => [7,4,6,1,2,3,5,8] => 1010000
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => [4,6,7,1,2,3,5,8] => 0010000
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => [3,7,2,6,1,4,5,8] => 0101000
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => [2,3,6,7,1,4,5,8] => 0001000
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => [7,3,6,1,2,4,5,8] => 1010000
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,3,2,4,6,7,5,8] => [3,6,7,1,2,4,5,8] => 0010000
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [2,1,3,4,6,7,5,8] => [2,6,7,1,3,4,5,8] => 0010000
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => [7,6,1,2,3,4,5,8] => 1100000
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => [6,7,1,2,3,4,5,8] => 0100000
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => [5,4,3,2,7,1,6,8] => 1110100
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [4,5,3,2,1,7,6,8] => [4,5,3,2,7,1,6,8] => 0110100
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [3,5,4,2,1,7,6,8] => [5,3,4,2,7,1,6,8] => 1010100
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [4,3,5,2,1,7,6,8] => [4,3,5,2,7,1,6,8] => 1010100
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [3,4,5,2,1,7,6,8] => [3,4,5,2,7,1,6,8] => 0010100
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => [3,5,2,4,7,1,6,8] => 0100100
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => [5,2,3,4,7,1,6,8] => 1000100
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [4,3,2,5,1,7,6,8] => [4,3,2,5,7,1,6,8] => 1100100
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => [2,3,4,5,7,1,6,8] => 0000100
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => [5,4,3,7,1,2,6,8] => 1101000
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => [4,5,3,7,1,2,6,8] => 0101000
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => [5,3,4,7,1,2,6,8] => 1001000
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => [4,3,5,7,1,2,6,8] => 1001000
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => [3,4,5,7,1,2,6,8] => 0001000
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => [5,2,4,7,1,3,6,8] => 1001000
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,2,5,4,3,7,6,8] => [5,4,7,1,2,3,6,8] => 1010000
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => [3,2,5,7,1,4,6,8] => 1001000
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [2,3,5,7,1,4,6,8] => 0001000
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [3,5,7,1,2,4,6,8] => 0010000
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [5,7,1,2,3,4,6,8] => 0100000
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => [4,3,2,7,1,5,6,8] => 1101000
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => [2,3,4,7,1,5,6,8] => 0001000
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => [4,7,1,2,3,5,6,8] => 0100000
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => [2,3,7,1,4,5,6,8] => 0010000
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [3,7,1,2,4,5,6,8] => 0100000
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => [2,7,1,3,4,5,6,8] => 0100000
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 1000000
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => 1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [5,6,4,3,2,1,7,8] => 0111100
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [5,4,6,3,2,1,7,8] => 1011100
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [4,5,6,3,2,1,7,8] => 0011100
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => [6,5,3,4,2,1,7,8] => 1101100
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [3,5,6,4,2,1,7,8] => [5,6,3,4,2,1,7,8] => 0101100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => [5,4,3,6,2,1,7,8] => 1101100
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => [3,4,5,6,2,1,7,8] => 0001100
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [2,5,4,6,3,1,7,8] => [5,4,6,2,3,1,7,8] => 1010100
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => [6,5,2,3,4,1,7,8] => 1100100
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [2,3,5,6,4,1,7,8] => [5,6,2,3,4,1,7,8] => 0100100
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => [4,3,6,2,5,1,7,8] => 1010100
[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [3,4,2,6,5,1,7,8] => [3,4,6,2,5,1,7,8] => 0010100
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => [4,6,2,3,5,1,7,8] => 0100100
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => [6,2,3,4,5,1,7,8] => 1000100
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7,8] => 1110100
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7,8] => 0110100
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [4,3,5,2,6,1,7,8] => 1010100
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [3,4,5,2,6,1,7,8] => 0010100
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => [5,2,3,4,6,1,7,8] => 1000100
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [4,3,2,5,6,1,7,8] => 1100100
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => [3,4,2,5,6,1,7,8] => 0100100
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [2,4,3,5,6,1,7,8] => [4,2,3,5,6,1,7,8] => 1000100
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => [3,2,4,5,6,1,7,8] => 1000100
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7,8] => 0000100
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => [6,5,4,3,1,2,7,8] => 1111000
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => [6,4,5,3,1,2,7,8] => 1011000
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => [5,4,6,3,1,2,7,8] => 1011000
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => [5,6,3,4,1,2,7,8] => 0101000
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => [4,6,3,5,1,2,7,8] => 0101000
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => [5,4,3,6,1,2,7,8] => 1101000
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => [4,3,5,6,1,2,7,8] => 1001000
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => [3,4,5,6,1,2,7,8] => 0001000
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [2,1,4,6,5,3,7,8] => [6,2,4,5,1,3,7,8] => 1001000
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [2,1,4,5,6,3,7,8] => [2,4,5,6,1,3,7,8] => 0001000
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => [6,5,4,1,2,3,7,8] => 1110000
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => [4,5,6,1,2,3,7,8] => 0010000
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => [3,6,2,5,1,4,7,8] => 0101000
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [3,2,1,5,6,4,7,8] => [3,2,5,6,1,4,7,8] => 1001000
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [2,3,1,5,6,4,7,8] => [2,3,5,6,1,4,7,8] => 0001000
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => [6,3,5,1,2,4,7,8] => 1010000
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => [3,5,6,1,2,4,7,8] => 0010000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [4,3,2,6,1,5,7,8] => 1101000
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => [3,2,4,6,1,5,7,8] => 1001000
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => [2,3,4,6,1,5,7,8] => 0001000
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => [2,4,6,1,3,5,7,8] => 0010000
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [4,6,1,2,3,5,7,8] => 0100000
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [3,2,1,4,6,5,7,8] => [3,2,6,1,4,5,7,8] => 1010000
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [2,3,1,4,6,5,7,8] => [2,3,6,1,4,5,7,8] => 0010000
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => [3,6,1,2,4,5,7,8] => 0100000
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => [2,6,1,3,4,5,7,8] => 0100000
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => 1000000
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => 1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => [4,5,3,2,1,6,7,8] => 0111000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => [5,3,4,2,1,6,7,8] => 1011000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => [4,3,5,2,1,6,7,8] => 1011000
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [3,4,5,2,1,6,7,8] => 0011000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => [5,4,2,3,1,6,7,8] => 1101000
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => [4,5,2,3,1,6,7,8] => 0101000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => [3,5,2,4,1,6,7,8] => 0101000
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => [5,2,3,4,1,6,7,8] => 1001000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => [4,3,2,5,1,6,7,8] => 1101000
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [3,4,2,5,1,6,7,8] => 0101000
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => [4,2,3,5,1,6,7,8] => 1001000
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => [3,2,4,5,1,6,7,8] => 1001000
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => 0001000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => [5,4,3,1,2,6,7,8] => 1110000
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,3,5,4,2,6,7,8] => [5,3,4,1,2,6,7,8] => 1010000
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,4,3,5,2,6,7,8] => [4,3,5,1,2,6,7,8] => 1010000
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => [3,4,5,1,2,6,7,8] => 0010000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => [5,2,4,1,3,6,7,8] => 1010000
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => [2,4,5,1,3,6,7,8] => 0010000
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => [5,4,1,2,3,6,7,8] => 1100000
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,2,4,5,3,6,7,8] => [4,5,1,2,3,6,7,8] => 0100000
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => [3,2,5,1,4,6,7,8] => 1010000
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => [2,3,5,1,4,6,7,8] => 0010000
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [3,5,1,2,4,6,7,8] => 0100000
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => [2,5,1,3,4,6,7,8] => 0100000
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 1000000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [3,4,2,1,5,6,7,8] => 0110000
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => 1010000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => 1010000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => 0010000
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => [4,3,1,2,5,6,7,8] => 1100000
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => 0100000
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => [2,4,1,3,5,6,7,8] => 0100000
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => 1000000
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => 1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => 0100000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => 1000000
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1000000
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [8,9,7,6,5,4,3,2,1] => 01111111
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [7,8,9,6,5,4,3,2,1] => 00111111
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [6,7,8,9,5,4,3,2,1] => 00011111
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [5,6,7,8,9,4,3,2,1] => 00001111
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [4,5,6,7,8,9,3,2,1] => 00000111
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [3,4,5,6,7,8,9,2,1] => 00000011
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1] => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [9,10,8,7,6,5,4,3,2,1] => 011111111
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [7,9,8,6,5,4,3,2,1] => [9,7,8,6,5,4,3,2,1] => 10111111
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [8,9,10,7,6,5,4,3,2,1] => 001111111
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [6,8,9,7,5,4,3,2,1] => [8,9,6,7,5,4,3,2,1] => 01011111
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [7,8,9,10,6,5,4,3,2,1] => 000111111
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [6,7,8,9,10,5,4,3,2,1] => 000011111
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [5,6,7,8,9,10,4,3,2,1] => 000001111
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [4,5,6,7,8,9,10,3,2,1] => 000000111
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [2,4,5,6,7,8,9,3,1] => [4,5,6,7,8,9,2,3,1] => 00000101
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [3,4,5,6,7,8,9,10,2,1] => 000000011
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => [3,4,5,6,7,8,9,1,2] => 00000010
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1] => 000000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [8,7,9,6,5,4,3,2,1] => 10111111
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [8,7,6,9,5,4,3,2,1] => 11011111
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [8,7,6,5,9,4,3,2,1] => 11101111
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [8,7,6,5,4,9,3,2,1] => 11110111
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [8,7,6,5,4,3,9,2,1] => 11111011
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,9,1] => 11111101
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 11111110
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [9,8,10,7,6,5,4,3,2,1] => 101111111
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [6,8,7,9,5,4,3,2,1] => [8,6,7,9,5,4,3,2,1] => 10011111
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [9,8,7,10,6,5,4,3,2,1] => 110111111
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [5,8,7,6,9,4,3,2,1] => [8,7,5,6,9,4,3,2,1] => 11001111
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [9,8,7,6,10,5,4,3,2,1] => 111011111
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [4,8,7,6,5,9,3,2,1] => [8,7,6,4,5,9,3,2,1] => 11100111
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [9,8,7,6,5,10,4,3,2,1] => 111101111
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [3,8,7,6,5,4,9,2,1] => [8,7,6,5,3,4,9,2,1] => 11110011
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [9,8,7,6,5,4,10,3,2,1] => 111110111
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [2,8,7,6,5,4,3,9,1] => [8,7,6,5,4,2,3,9,1] => 11111001
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [9,8,7,6,5,4,3,10,2,1] => 111111011
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9] => [8,7,6,5,4,3,1,2,9] => 11111100
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,10,1] => 111111101
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => 111111110
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,3,5,7,9,10,8,6,4,2] => [9,10,7,8,5,6,3,4,1,2] => 010101010
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [5,6,4,7,3,8,2,9,1,10] => 010101010
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [1,3,5,7,9,11,12,10,8,6,4,2] => [11,12,9,10,7,8,5,6,3,4,1,2] => 01010101010
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => [2,4,6,8,10,1,3,5,7,9] => 000010000
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,4,6,8,10,12,1,3,5,7,9,11] => 00000100000
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => 10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => 100000000
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,9,8] => [2,9,1,3,4,5,6,7,8] => 01000000
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,1] => 10000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => [11,1,2,3,4,5,6,7,8,9,10] => 1000000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,8,10,9] => [2,10,1,3,4,5,6,7,8,9] => 010000000
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,3,2,4,5,6,7,9,8] => [3,9,1,2,4,5,6,7,8] => 01000000
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [2,3,1,4,5,6,7,9,8] => [2,3,9,1,4,5,6,7,8] => 00100000
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [2,4,3,5,6,7,8,9,1] => [4,2,3,5,6,7,8,9,1] => 10000001
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [3,4,2,5,6,7,8,9,1] => 01000001
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [3,2,4,5,6,7,8,9,10,1] => 100000001
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => [8,9,1,2,3,4,5,6,7] => 01000000
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => [7,8,9,1,2,3,4,5,6] => 00100000
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,6,7,8,9,5] => [6,7,8,9,1,2,3,4,5] => 00010000
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,5,6,7,8,9,4] => [5,6,7,8,9,1,2,3,4] => 00001000
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,3] => [4,5,6,7,8,9,1,2,3] => 00000100
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => [9,8,1,2,3,4,5,6,7] => 11000000
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => [9,10,1,2,3,4,5,6,7,8] => 010000000
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,5,8,7,9,6] => [8,7,9,1,2,3,4,5,6] => 10100000
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,6,8,9,10,7] => [8,9,10,1,2,3,4,5,6,7] => 001000000
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,4,7,6,8,9,5] => [7,6,8,9,1,2,3,4,5] => 10010000
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,5,7,8,9,10,6] => [7,8,9,10,1,2,3,4,5,6] => 000100000
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [1,2,3,6,5,7,8,9,4] => [6,5,7,8,9,1,2,3,4] => 10001000
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,4,6,7,8,9,10,5] => [6,7,8,9,10,1,2,3,4,5] => 000010000
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [1,2,5,4,6,7,8,9,3] => [5,4,6,7,8,9,1,2,3] => 10000100
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,3,5,6,7,8,9,10,4] => [5,6,7,8,9,10,1,2,3,4] => 000001000
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,4,3,5,6,7,8,9,2] => [4,3,5,6,7,8,9,1,2] => 10000010
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,10,3] => [4,5,6,7,8,9,10,1,2,3] => 000000100
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,10,2] => [3,4,5,6,7,8,9,10,1,2] => 000000010
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => 11111110
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [7,8,6,5,4,3,2,1,9] => 01111110
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => [8,9,7,6,5,4,3,1,2] => 01111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,1,2] => 111111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => 1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [8,9,7,6,5,4,3,2,1,10] => 011111110
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [7,6,8,5,4,3,2,1,9] => 10111110
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => [8,7,9,6,5,4,3,1,2] => 10111110
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => [9,10,8,7,6,5,4,3,1,2] => 011111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => [11,10,9,8,7,6,5,4,3,1,2] => 1111111110
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => [6,5,7,4,8,3,9,2,10,1] => 101010101
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => [9,8,7,6,5,2,4,1,3] => 11111010
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [3,2,1,9,8,7,6,5,4] => [9,8,7,3,6,2,5,1,4] => 11101010
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [4,3,2,1,9,8,7,6,5] => [9,4,8,3,7,2,6,1,5] => 10101010
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [5,4,3,2,1,9,8,7,6] => [5,4,9,3,8,2,7,1,6] => 10101010
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [6,5,4,3,2,1,9,8,7] => [6,5,4,3,9,2,8,1,7] => 11101010
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => [7,6,5,4,3,2,9,1,8] => 11111010
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => [9,8,7,6,5,4,1,2,3] => 11111100
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,2,4,1,3] => 111111010
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [3,2,1,10,9,8,7,6,5,4] => [10,9,8,7,3,6,2,5,1,4] => 111101010
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => [10,9,4,8,3,7,2,6,1,5] => 110101010
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [5,4,3,2,1,10,9,8,7,6] => [5,10,4,9,3,8,2,7,1,6] => 010101010
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,10,3,9,2,8,1,7] => 110101010
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [7,6,5,4,3,2,1,10,9,8] => [7,6,5,4,3,10,2,9,1,8] => 111101010
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,10,1,9] => 111111010
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => 11111100
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => 11111000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => 11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 11100000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => 11000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => 111111100
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => 111111000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => 111110000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => 111100000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => 111000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,4,3,2,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => 11000000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => 110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => 10000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => 100000000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [4,9,8,7,6,5,3,2,1] => [9,8,7,6,4,5,3,2,1] => 11110111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [3,9,8,7,6,5,4,2,1] => [9,8,7,6,5,3,4,2,1] => 11111011
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => [9,8,7,6,5,4,2,3,1] => 11111101
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [6,10,9,8,7,5,4,3,2,1] => [10,9,8,6,7,5,4,3,2,1] => 111011111
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,8,1] => 10000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => 1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [2,1,3,4,5,6,8,7,9] => [2,8,1,3,4,5,6,7,9] => 01000000
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [2,1,3,4,5,6,8,9,7] => [2,8,9,1,3,4,5,6,7] => 00100000
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [2,3,4,5,6,8,9,7,1] => [8,9,2,3,4,5,6,7,1] => 01000001
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,8,10,9,1] => [10,2,3,4,5,6,7,8,9,1] => 100000001
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [2,1,4,3,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => 01000000
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [3,2,1,5,4,6,7,8,9] => [3,2,5,1,4,6,7,8,9] => 10100000
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [6,5,4,3,2,1,8,7,9] => [6,5,4,3,2,8,1,7,9] => 11110100
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => [3,4,5,6,7,8,2,9,1] => 00000101
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1,9] => 00000010
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => 01000000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8,9] => 00000100
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => 010000000
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [2,4,3,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => 10100000
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [2,3,5,4,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => 10010000
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [2,3,4,6,5,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => 10001000
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [2,3,4,5,7,6,1,8,9] => [7,2,3,4,5,6,1,8,9] => 10000100
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [2,3,4,5,6,8,7,1,9] => [8,2,3,4,5,6,7,1,9] => 10000010
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1,10] => 000000010
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => 10000000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => 10000000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,6,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => 10000000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,7,6,8,9] => [7,1,2,3,4,5,6,8,9] => 10000000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => 10000000
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => 100000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => 100000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,2,3,5,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => 100000000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,2,3,4,6,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => 100000000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,5,7,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => 100000000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,6,8,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => 100000000
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => 100000000
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [1,3,4,5,6,7,9,8,2] => [9,3,4,5,6,7,8,1,2] => 10000010
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [7,6,5,4,3,2,9,8,1] => [7,6,5,4,3,9,2,8,1] => 11110101
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,1] => [4,3,2,5,6,7,8,9,1] => 11000001
[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [5,4,3,2,6,7,8,9,1] => [5,4,3,2,6,7,8,9,1] => 11100001
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => [6,5,4,3,2,7,8,9,1] => 11110001
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [7,6,5,4,3,2,8,9,1] => [7,6,5,4,3,2,8,9,1] => 11111001
[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,10,1] => [4,3,2,5,6,7,8,9,10,1] => 110000001
[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]] => [5,4,3,2,6,7,8,9,10,1] => [5,4,3,2,6,7,8,9,10,1] => 111000001
[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => [6,5,4,3,2,7,8,9,10,1] => [6,5,4,3,2,7,8,9,10,1] => 111100001
[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]] => [7,6,5,4,3,2,8,9,10,1] => [7,6,5,4,3,2,8,9,10,1] => 111110001
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => [8,7,6,5,4,3,2,9,10,1] => [8,7,6,5,4,3,2,9,10,1] => 111111001
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,4,1,2,3] => 111111100
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,3,2,9,8,7,6,5,4] => [9,8,7,6,3,5,1,2,4] => 11110100
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10] => [9,8,7,6,5,4,3,1,2,10] => 111111100
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [2,8,7,9,6,5,4,3,1] => [8,7,9,6,5,4,2,3,1] => 10111101
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,3,4,5,2,6,7,8,9] => [3,4,5,1,2,6,7,8,9] => 00100000
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [2,1,4,5,6,7,8,9,3] => [2,4,5,6,7,8,9,1,3] => 00000010
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,3,4,5,6,7,8,2,9] => [3,4,5,6,7,8,1,2,9] => 00000100
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => [10,9,1,2,3,4,5,6,7,8] => 110000000
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => [6,7,8,5,4,3,2,1,9] => 00111110
[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.] => [6,5,7,8,4,3,2,1,9] => [6,5,7,8,4,3,2,1,9] => 10011110
[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.] => [6,5,4,7,8,3,2,1,9] => [6,5,4,7,8,3,2,1,9] => 11001110
[[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.] => [6,5,4,3,7,8,2,1,9] => [6,5,4,3,7,8,2,1,9] => 11100110
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [6,5,4,3,2,7,8,1,9] => [6,5,4,3,2,7,8,1,9] => 11110010
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => [7,8,9,6,5,4,3,2,1,10] => 001111110
[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => [7,6,8,9,5,4,3,2,1,10] => [7,6,8,9,5,4,3,2,1,10] => 100111110
[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.] => [7,6,5,8,9,4,3,2,1,10] => [7,6,5,8,9,4,3,2,1,10] => 110011110
[[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.] => [7,6,5,4,8,9,3,2,1,10] => [7,6,5,4,8,9,3,2,1,10] => 111001110
[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.] => [7,6,5,4,3,8,9,2,1,10] => [7,6,5,4,3,8,9,2,1,10] => 111100110
[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.] => [7,6,5,4,3,2,8,9,1,10] => [7,6,5,4,3,2,8,9,1,10] => 111110010
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => [9,8,7,1,2,3,4,5,6] => 11100000
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => [9,8,7,6,1,2,3,4,5] => 11110000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => [9,8,7,6,5,1,2,3,4] => 11111000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,7,6,9,8] => [7,9,1,2,3,4,5,6,8] => 01000000
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => [10,9,8,1,2,3,4,5,6,7] => 111000000
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,4,6,5,9,8,7] => [9,6,8,1,2,3,4,5,7] => 10100000
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => [10,9,8,7,1,2,3,4,5,6] => 111100000
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,3,5,4,9,8,7,6] => [9,8,5,7,1,2,3,4,6] => 11010000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => [10,9,8,7,6,1,2,3,4,5] => 111110000
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,2,4,3,9,8,7,6,5] => [9,8,7,4,6,1,2,3,5] => 11101000
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => [10,9,8,7,6,5,1,2,3,4] => 111111000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,6,8,7,10,9] => [8,10,1,2,3,4,5,6,7,9] => 010000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => [10,9,11,8,7,6,5,4,3,2,1] => 1011111111
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [1,9,8,10,7,6,5,4,3,2] => [9,8,10,7,6,5,4,3,1,2] => 101111110
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [2,8,9,7,6,5,4,3,1] => [8,9,7,6,5,4,2,3,1] => 01111101
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => [10,11,9,8,7,6,5,4,3,2,1] => 0111111111
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => [7,8,6,5,4,3,2,9,1] => 01111101
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => [3,4,2,1,5,6,7,8,9] => 01100000
[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10,11] => [2,3,1,4,5,6,7,8,9,10,11] => 0100000000
[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9,10] => [3,4,2,1,5,6,7,8,9,10] => 011000000
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => [3,4,2,5,1,6,7,8,9] => 01010000
[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => 1000000000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => [7,6,5,4,3,2,8,1,9] => 11111010
[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.] => [5,8,7,6,4,3,2,1,9] => [8,7,5,6,4,3,2,1,9] => 11011110
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [7,6,5,8,4,3,2,1,9] => [7,6,5,8,4,3,2,1,9] => 11011110
[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.] => [6,7,5,8,4,3,2,1,9] => [6,7,5,8,4,3,2,1,9] => 01011110
[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.] => [4,9,8,7,6,5,3,2,1,10] => [9,8,7,6,4,5,3,2,1,10] => 111101110
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [2,3,1,5,4,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => 00100000
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => [4,5,3,2,1,6,7,8,9] => 01110000
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => [3,2,4,5,6,7,8,1,9] => 10000010
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [5,4,3,2,1,8,7,6,9] => [5,4,3,8,2,7,1,6,9] => 11010100
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [7,6,5,4,3,2,1,9,8,10] => [7,6,5,4,3,2,9,1,8,10] => 111110100
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [2,3,9,8,7,6,5,4,1] => [9,8,7,6,5,2,3,4,1] => 11111001
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [2,8,7,6,5,4,3,1,9] => [8,7,6,5,4,2,3,1,9] => 11111010
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [2,3,4,5,6,7,1,9,8] => [2,3,4,5,6,7,9,1,8] => 00000010
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,3,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => 01000000
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [8,7,6,5,4,3,2,9,1,10] => [8,7,6,5,4,3,2,9,1,10] => 111111010
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [1,4,5,6,7,8,3,9,2] => [4,5,6,7,8,3,9,1,2] => 00001010
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,2,8,7,6,5,4,3,9] => [8,7,6,5,4,1,2,3,9] => 11111000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,8,10,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => 1000000000
[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => [2,1,3,5,6,7,8,9,4] => [2,5,6,7,8,9,1,3,4] => 00000100
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.] => [5,6,4,3,2,1,7,8,9] => [5,6,4,3,2,1,7,8,9] => 01111000
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [5,6,4,3,2,1,7,8,9,10] => [5,6,4,3,2,1,7,8,9,10] => 011110000
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.] => [6,7,5,4,3,2,1,8,9,10,11] => [6,7,5,4,3,2,1,8,9,10,11] => 0111110000
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.] => [6,7,5,4,3,2,1,8,9,10] => [6,7,5,4,3,2,1,8,9,10] => 011111000
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.] => [5,6,4,3,2,7,1,8,9] => [5,6,4,3,2,7,1,8,9] => 01110100
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [1,2,5,6,7,4,8,9,3] => [5,6,7,4,8,9,1,2,3] => 00100100
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => [6,7,5,4,3,2,1,8,9] => 01111100
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
See Mp00067Foata bijection.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
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