Identifier
Mp00012:
Binary trees
—to Dyck path: up step, left tree, down step, right tree⟶
Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
[.,.] => [1,0] => [1] =>
[.,[.,.]] => [1,0,1,0] => [1,2] => 1
[[.,.],.] => [1,1,0,0] => [2,1] => 0
[.,[.,[.,.]]] => [1,0,1,0,1,0] => [1,2,3] => 11
[.,[[.,.],.]] => [1,0,1,1,0,0] => [1,3,2] => 10
[[.,.],[.,.]] => [1,1,0,0,1,0] => [2,1,3] => 01
[[.,[.,.]],.] => [1,1,0,1,0,0] => [2,3,1] => 00
[[[.,.],.],.] => [1,1,1,0,0,0] => [3,2,1] => 00
[.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 111
[.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 110
[.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 101
[.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 100
[.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 100
[[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 011
[[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 010
[[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 001
[[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 001
[[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 000
[[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => 000
[[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 000
[[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 000
[[[[.,.],.],.],.] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 000
[.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 1111
[.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1110
[.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 1101
[.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1100
[.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1100
[.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 1011
[.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1010
[.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 1001
[.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1001
[.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000
[.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000
[.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000
[.,[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000
[.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000
[[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 0111
[[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 0110
[[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 0101
[[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100
[[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100
[[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 0011
[[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010
[[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0011
[[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010
[[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001
[[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001
[[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001
[[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001
[[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 0000
[[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => 0000
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => 0000
[[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => 0000
[[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0000
[[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0000
[[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 0000
[[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0000
[[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0000
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0000
[[[.,[[.,.],.]],.],.] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => 0000
[[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => 0000
[[[[.,[.,.]],.],.],.] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 0000
[[[[[.,.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0000
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 11111
[.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 11110
[.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 11101
[.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 11100
[.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 11100
[.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 11011
[.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 11010
[.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 11001
[.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 11001
[.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 11000
[.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 11000
[.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 11000
[.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 11000
[.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 11000
[.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 10111
[.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 10110
[.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 10101
[.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 10100
[.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 10100
[.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 10011
[.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 10010
[.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 10011
[.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 10010
[.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 10001
[.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 10001
[.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 10001
[.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => 10001
[.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 10001
[.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 10000
[.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 10000
[.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 10000
[.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 10000
[.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 10000
[.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 10000
[.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 10000
[.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 10000
[.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 10000
>>> Load all 1544 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 10000
[.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 10000
[.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 10000
[.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 10000
[.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 10000
[[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 01111
[[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 01110
[[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 01101
[[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 01100
[[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 01100
[[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 01011
[[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 01010
[[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 01001
[[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 01001
[[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 01000
[[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 01000
[[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 01000
[[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 01000
[[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 01000
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 00111
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 00110
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 00101
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 00100
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 00100
[[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 00111
[[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 00110
[[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 00101
[[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 00100
[[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 00100
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 00011
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 00010
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 00011
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 00010
[[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 00011
[[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 00010
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => 00011
[[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => 00010
[[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 00011
[[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 00010
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 00001
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 00001
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 00001
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => 00001
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 00001
[[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 00001
[[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 00001
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => 00001
[[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 00001
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => 00001
[[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => 00001
[[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => 00001
[[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 00001
[[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 00001
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 00000
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => 00000
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => 00000
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => 00000
[[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 00000
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => 00000
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 00000
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => 00000
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 00000
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => 00000
[[.,[[.,[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => 00000
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => 00000
[[.,[[[.,[.,.]],.],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => 00000
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 00000
[[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 00000
[[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 00000
[[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 00000
[[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => 00000
[[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 00000
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 00000
[[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => 00000
[[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 00000
[[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 00000
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => 00000
[[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => 00000
[[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 00000
[[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => 00000
[[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 00000
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => 00000
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => 00000
[[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => 00000
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => 00000
[[[.,[[[.,.],.],.]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => 00000
[[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => 00000
[[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => 00000
[[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => 00000
[[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => 00000
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => 00000
[[[[.,[[.,.],.]],.],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => 00000
[[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => 00000
[[[[[.,[.,.]],.],.],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => 00000
[[[[[[.,.],.],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 111110
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 111101
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 111100
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 111100
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => 111011
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => 111010
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => 111001
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => 111001
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 111000
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => 111000
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 111000
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => 111000
[.,[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 111000
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => 110111
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => 110110
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => 110101
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => 110100
[.,[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => 110100
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => 110011
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => 110010
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => 110011
[.,[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => 110010
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => 110001
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => 110001
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => 110001
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => 110001
[.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 110001
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 110000
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => 110000
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => 110000
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => 110000
[.,[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 110000
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 110000
[.,[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => 110000
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 110000
[.,[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 110000
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => 110000
[.,[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => 110000
[.,[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => 110000
[.,[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => 110000
[.,[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 110000
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 101111
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => 101110
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => 101101
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => 101100
[.,[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => 101100
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => 101011
[.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => 101010
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => 101001
[.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => 101001
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => 101000
[.,[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => 101000
[.,[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => 101000
[.,[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => 101000
[.,[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 101000
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => 100111
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => 100110
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => 100101
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => 100100
[.,[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => 100100
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => 100111
[.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => 100110
[.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => 100101
[.,[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => 100100
[.,[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 100100
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => 100011
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => 100010
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => 100011
[.,[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => 100010
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => 100011
[.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => 100010
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => 100011
[.,[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => 100010
[.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => 100011
[.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => 100010
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => 100001
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => 100001
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => 100001
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => 100001
[.,[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 100001
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => 100001
[.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => 100001
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => 100001
[.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => 100001
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => 100001
[.,[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => 100001
[.,[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => 100001
[.,[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => 100001
[.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => 100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 100000
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => 100000
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => 100000
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => 100000
[.,[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 100000
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => 100000
[.,[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => 100000
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => 100000
[.,[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 100000
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => 100000
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => 100000
[.,[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => 100000
[.,[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => 100000
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 100000
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 100000
[.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => 100000
[.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => 100000
[.,[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => 100000
[.,[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 100000
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => 100000
[.,[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => 100000
[.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => 100000
[.,[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => 100000
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => 100000
[.,[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => 100000
[.,[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => 100000
[.,[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => 100000
[.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => 100000
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => 100000
[.,[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => 100000
[.,[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => 100000
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => 100000
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 100000
[.,[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => 100000
[.,[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => 100000
[.,[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => 100000
[.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => 100000
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 100000
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 100000
[.,[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 100000
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 100000
[.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 100000
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 011111
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => 011110
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => 011101
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => 011100
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => 011100
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => 011011
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => 011010
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => 011001
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => 011001
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => 011000
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => 011000
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => 011000
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => 011000
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => 011000
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => 010111
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => 010110
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => 010101
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => 010100
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => 010100
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => 010011
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => 010010
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => 010011
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => 010010
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => 010001
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => 010001
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => 010001
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => 010001
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => 010001
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => 010000
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => 010000
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => 010000
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => 010000
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => 010000
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => 010000
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => 010000
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => 010000
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => 010000
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => 010000
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => 010000
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => 010000
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => 010000
[[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 010000
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => 001111
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => 001110
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => 001101
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => 001100
[[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => 001100
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => 001011
[[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => 001010
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => 001001
[[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => 001001
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => 001000
[[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => 001000
[[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => 001000
[[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => 001000
[[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => 001000
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => 001111
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => 001110
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => 001101
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => 001100
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => 001100
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => 001011
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => 001010
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => 001001
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => 001001
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => 001000
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => 001000
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => 001000
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => 001000
[[[.,.],.],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => 001000
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => 000111
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => 000110
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => 000101
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => 000100
[[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => 000100
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => 000111
[[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => 000110
[[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => 000101
[[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => 000100
[[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => 000100
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => 000111
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => 000110
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => 000101
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => 000100
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => 000100
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => 000111
[[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => 000110
[[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => 000101
[[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => 000100
[[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => 000100
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => 000111
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => 000110
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => 000101
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => 000100
[[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => 000100
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => 000011
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => 000010
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => 000011
[[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => 000010
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => 000011
[[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => 000010
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => 000011
[[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => 000010
[[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => 000011
[[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => 000010
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => 000011
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => 000010
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => 000011
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => 000010
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => 000011
[[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => 000010
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => 000011
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => 000010
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => 000011
[[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => 000010
[[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => 000011
[[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => 000010
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => 000011
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => 000010
[[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => 000011
[[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => 000010
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => 000011
[[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 000010
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => 000001
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => 000001
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => 000001
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => 000001
[[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => 000001
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => 000001
[[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => 000001
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => 000001
[[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => 000001
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => 000001
[[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => 000001
[[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => 000001
[[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => 000001
[[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => 000001
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => 000001
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => 000001
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => 000001
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => 000001
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => 000001
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => 000001
[[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => 000001
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => 000001
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => 000001
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => 000001
[[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => 000001
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => 000001
[[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => 000001
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 000001
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => 000001
[[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => 000001
[[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => 000001
[[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => 000001
[[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => 000001
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => 000001
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => 000001
[[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => 000001
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => 000001
[[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => 000001
[[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => 000001
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => 000001
[[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => 000001
[[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 000000
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => 000000
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => 000000
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => 000000
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => 000000
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => 000000
[[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => 000000
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => 000000
[[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => 000000
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => 000000
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => 000000
[[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => 000000
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => 000000
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => 000000
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => 000000
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => 000000
[[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => 000000
[[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => 000000
[[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => 000000
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => 000000
[[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => 000000
[[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => 000000
[[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => 000000
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => 000000
[[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => 000000
[[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => 000000
[[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => 000000
[[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => 000000
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => 000000
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => 000000
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => 000000
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => 000000
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => 000000
[[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => 000000
[[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => 000000
[[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => 000000
[[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => 000000
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => 000000
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => 000000
[[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => 000000
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => 000000
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => 000000
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => 000000
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => 000000
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => 000000
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => 000000
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => 000000
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => 000000
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => 000000
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => 000000
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => 000000
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => 000000
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => 000000
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => 000000
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => 000000
[[[.,.],[[[[.,.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => 000000
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => 000000
[[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => 000000
[[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => 000000
[[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => 000000
[[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => 000000
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => 000000
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => 000000
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => 000000
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => 000000
[[[[.,.],.],[[[.,.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => 000000
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => 000000
[[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => 000000
[[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => 000000
[[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => 000000
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => 000000
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => 000000
[[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => 000000
[[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => 000000
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => 000000
[[[[[.,.],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => 000000
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => 000000
[[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => 000000
[[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => 000000
[[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => 000000
[[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => 000000
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => 000000
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => 000000
[[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => 000000
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => 000000
[[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => 000000
[[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => 000000
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => 000000
[[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => 000000
[[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => 000000
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => 000000
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => 000000
[[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => 000000
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => 000000
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => 000000
[[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => 000000
[[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => 000000
[[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => 000000
[[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => 000000
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => 000000
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => 000000
[[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => 000000
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => 000000
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => 000000
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => 000000
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => 000000
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => 000000
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => 000000
[[[[.,.],[[[.,.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => 000000
[[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => 000000
[[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => 000000
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => 000000
[[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => 000000
[[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => 000000
[[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => 000000
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => 000000
[[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => 000000
[[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => 000000
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => 000000
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => 000000
[[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => 000000
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => 000000
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => 000000
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => 000000
[[[[[.,.],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => 000000
[[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => 000000
[[[[[[.,.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => 000000
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => 000000
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => 000000
[[[[[[.,.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => 000000
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => 000000
[[[[[[[.,.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => 000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1111110
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 1111101
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => 1111100
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => 1111100
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => 1111011
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => 1111010
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => 1111001
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => 1111001
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => 1111000
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => 1111000
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => 1111000
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => 1111000
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => 1111000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => 1110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => 1110110
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 1110101
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => 1110100
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => 1110100
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => 1110011
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => 1110010
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => 1110011
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => 1110010
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => 1110001
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => 1110001
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => 1110001
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => 1110001
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => 1110001
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 1110000
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => 1110000
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => 1110000
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => 1110000
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => 1110000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => 1110000
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => 1110000
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => 1110000
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => 1110000
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => 1110000
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => 1110000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => 1110000
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => 1110000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => 1110000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => 1101111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => 1101110
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => 1101101
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => 1101100
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => 1101100
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => 1101010
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => 1101001
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => 1101000
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => 1101000
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => 1101000
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => 1101000
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => 1100101
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => 1100100
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => 1100100
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => 1100111
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => 1100110
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => 1100100
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => 1100100
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => 1100011
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => 1100010
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => 1100011
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => 1100011
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => 1100001
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => 1100001
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => 1100001
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => 1100001
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => 1100000
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => 1100000
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => 1100000
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => 1100000
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => 1100000
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => 1100000
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => 1100000
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => 1100000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => 1100000
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => 1100000
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => 1100000
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => 1100000
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => 1100000
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => 1100000
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => 1100000
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => 1100000
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => 1100000
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => 1100000
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => 1100000
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => 1100000
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => 1100000
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => 1100000
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => 1100000
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => 1100000
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => 1100000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => 1100000
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => 1100000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => 1011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => 1011110
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 1011101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => 1011100
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => 1011100
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => 1011011
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => 1011010
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => 1011001
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => 1011000
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => 1011000
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => 1011000
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => 1011000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 1010111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1010101
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => 1010100
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => 1010100
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => 1010010
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => 1010011
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => 1010010
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => 1010001
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => 1010001
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => 1010000
[.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => 1010000
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => 1010000
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => 1010000
[.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => 1010000
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => 1010000
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => 1010000
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => 1010000
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => 1010000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => 1001111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => 1001110
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => 1001100
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => 1001010
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => 1001001
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => 1001000
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => 1001000
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => 1001000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => 1001111
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => 1001110
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => 1001101
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => 1001100
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => 1001100
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => 1001001
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1001001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => 1001000
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => 1001000
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => 1001000
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => 1001000
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => 1001000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => 1000111
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => 1000101
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => 1000100
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => 1000100
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => 1000110
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => 1000101
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => 1000100
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => 1000101
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => 1000111
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => 1000100
[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => 1000100
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => 1000100
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => 1000100
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => 1000011
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => 1000010
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => 1000010
[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => 1000010
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => 1000011
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => 1000011
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => 1000010
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => 1000011
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => 1000011
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => 1000011
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => 1000011
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => 1000010
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => 1000011
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => 1000010
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => 1000001
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => 1000001
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => 1000001
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => 1000001
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => 1000001
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => 1000001
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => 1000001
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => 1000001
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => 1000001
[.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => 1000001
[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => 1000001
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => 1000001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => 1000001
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => 1000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => 1000000
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => 1000000
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => 1000000
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => 1000000
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => 1000000
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => 1000000
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => 1000000
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => 1000000
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => 1000000
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => 1000000
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => 1000000
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => 1000000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => 1000000
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => 1000000
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => 1000000
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => 1000000
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => 1000000
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => 1000000
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => 1000000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => 1000000
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => 1000000
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => 1000000
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => 1000000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => 1000000
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => 1000000
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => 1000000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => 1000000
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => 1000000
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => 1000000
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => 1000000
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => 1000000
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => 1000000
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => 1000000
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => 1000000
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => 1000000
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => 1000000
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => 1000000
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => 1000000
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => 1000000
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => 1000000
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => 1000000
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => 1000000
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => 1000000
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => 1000000
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => 1000000
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => 1000000
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => 1000000
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => 1000000
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => 1000000
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => 1000000
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => 1000000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => 1000000
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => 1000000
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => 1000000
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => 1000000
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => 1000000
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => 1000000
[.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => 1000000
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => 1000000
[.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => 1000000
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => 1000000
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => 1000000
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => 1000000
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => 1000000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => 1000000
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => 1000000
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => 1000000
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => 1000000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => 1000000
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 1000000
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => 1000000
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 1000000
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 1000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => 0111111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => 0111101
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => 0111100
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => 0111100
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => 0111011
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => 0111010
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => 0111000
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => 0111000
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => 0111000
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => 0110111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => 0110110
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => 0110100
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => 0110100
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => 0110010
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => 0110010
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => 0110000
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => 0110000
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => 0110000
[[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => 0110000
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => 0110000
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => 0110000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => 0101111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => 0101110
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => 0101100
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => 0101100
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => 0101011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 0101010
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => 0101001
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => 0101000
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 0101000
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => 0100111
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => 0100100
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => 0100111
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => 0100110
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => 0100101
[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => 0100100
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => 0100010
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => 0100011
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => 0100010
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => 0100010
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 0100010
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => 0100001
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => 0100001
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => 0100001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => 0100000
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => 0100000
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => 0100000
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => 0100000
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => 0100000
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => 0100000
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => 0100000
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => 0100000
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => 0100000
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => 0100000
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => 0100000
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => 0100000
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => 0100000
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => 0100000
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => 0100000
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => 0100000
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => 0100000
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => 0100000
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => 0100000
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => 0100000
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => 0100000
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => 0100000
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => 0100000
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => 0100000
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => 0100000
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 0100000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => 0011111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => 0011110
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => 0011101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => 0011100
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => 0011010
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => 0011000
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => 0011000
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => 0010111
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => 0010101
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => 0010011
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => 0010011
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => 0010010
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => 0010001
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => 0010001
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => 0010000
[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => 0010000
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => 0010000
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => 0010000
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => 0010000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => 0011111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => 0011110
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => 0011101
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => 0011100
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => 0011100
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => 0011001
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => 0011000
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => 0011000
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => 0011000
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => 0010111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => 0010101
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => 0010011
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => 0010011
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => 0010010
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => 0010001
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => 0010001
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => 0010001
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => 0010001
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => 0010000
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => 0010000
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => 0010000
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => 0010000
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => 0010000
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => 0010000
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => 0010000
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => 0010000
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => 0010000
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => 0010000
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => 0010000
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => 0010000
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => 0010000
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 0010000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => 0001111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => 0001110
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => 0001011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => 0001010
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => 0001001
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => 0001001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => 0001000
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => 0001000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => 0001111
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => 0001100
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => 0001011
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => 0001000
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => 0001000
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => 0001111
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => 0001100
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => 0001011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => 0001010
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => 0001000
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => 0001000
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => 0001000
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => 0001000
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => 0001111
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => 0001101
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => 0001100
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => 0001011
[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => 0001001
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => 0001000
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => 0001000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => 0001111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => 0001110
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => 0001101
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => 0001100
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => 0001100
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => 0001011
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 0001010
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => 0001001
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => 0001001
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => 0001000
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => 0001000
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => 0001000
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => 0001000
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => 0000111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => 0000110
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => 0000101
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => 0000100
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => 0000100
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => 0000111
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => 0000110
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => 0000101
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => 0000100
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => 0000111
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => 0000110
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => 0000101
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => 0000100
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => 0000111
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => 0000100
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => 0000111
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => 0000110
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => 0000100
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => 0000111
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => 0000100
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => 0000111
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => 0000110
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => 0000101
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => 0000100
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => 0000100
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => 0000111
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => 0000110
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => 0000100
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => 0000100
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => 0000111
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => 0000100
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => 0000111
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => 0000100
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => 0000100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => 0000111
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => 0000110
[[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => 0000101
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => 0000100
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => 0000111
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => 0000110
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => 0000101
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => 0000100
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => 0000111
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => 0000110
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => 0000100
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => 0000100
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => 0000111
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => 0000110
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => 0000101
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => 0000100
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 0000100
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => 0000011
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => 0000010
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => 0000011
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => 0000011
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => 0000010
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => 0000011
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => 0000010
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => 0000011
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => 0000010
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => 0000011
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => 0000010
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => 0000011
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => 0000010
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => 0000011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => 0000010
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => 0000011
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => 0000010
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => 0000011
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => 0000010
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => 0000011
[[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => 0000010
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => 0000011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => 0000010
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => 0000011
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => 0000010
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => 0000011
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => 0000011
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => 0000010
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => 0000011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => 0000011
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => 0000010
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => 0000011
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => 0000010
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => 0000011
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => 0000010
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => 0000010
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => 0000010
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => 0000010
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => 0000011
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => 0000010
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => 0000011
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 0000010
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => 0000001
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => 0000001
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => 0000001
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => 0000001
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => 0000001
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => 0000001
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => 0000001
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => 0000001
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => 0000001
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => 0000001
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => 0000001
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => 0000001
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => 0000001
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => 0000001
[[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => 0000001
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => 0000001
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => 0000001
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => 0000001
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => 0000001
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => 0000001
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => 0000001
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => 0000001
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => 0000001
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => 0000001
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => 0000001
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => 0000001
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => 0000001
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => 0000001
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => 0000001
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => 0000001
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => 0000001
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => 0000001
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => 0000001
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => 0000001
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => 0000001
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => 0000001
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => 0000001
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => 0000001
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => 0000001
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => 0000001
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => 0000001
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => 0000001
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => 0000001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => 0000001
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => 0000001
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => 0000001
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => 0000001
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => 0000001
[[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => 0000001
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => 0000001
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => 0000001
[[[[.,[[.,.],.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => 0000001
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => 0000001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => 0000001
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => 0000001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => 0000001
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => 0000001
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => 0000001
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => 0000001
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => 0000001
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => 0000001
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => 0000001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => 0000001
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => 0000001
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => 0000001
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => 0000001
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 0000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 0000000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => 0000000
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => 0000000
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => 0000000
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => 0000000
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => 0000000
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => 0000000
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => 0000000
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => 0000000
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => 0000000
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => 0000000
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => 0000000
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => 0000000
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => 0000000
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => 0000000
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => 0000000
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => 0000000
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => 0000000
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => 0000000
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => 0000000
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => 0000000
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => 0000000
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => 0000000
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => 0000000
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => 0000000
[[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => 0000000
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => 0000000
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => 0000000
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => 0000000
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => 0000000
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => 0000000
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => 0000000
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => 0000000
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => 0000000
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => 0000000
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => 0000000
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => 0000000
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => 0000000
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => 0000000
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => 0000000
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => 0000000
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => 0000000
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => 0000000
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => 0000000
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,6,3,5,4,7,8,1] => 0000000
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => 0000000
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => 0000000
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => 0000000
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => 0000000
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => 0000000
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => 0000000
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => 0000000
[[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => 0000000
[[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => 0000000
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => 0000000
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => 0000000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => 0000000
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => 0000000
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => 0000000
[[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => 0000000
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => 0000000
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => 0000000
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => 0000000
[[.,[[[[.,.],.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => 0000000
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => 0000000
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => 0000000
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => 0000000
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => 0000000
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => 0000000
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => 0000000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => 0000000
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => 0000000
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => 0000000
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => 0000000
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => 0000000
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => 0000000
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => 0000000
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => 0000000
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => 0000000
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => 0000000
[[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => 0000000
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => 0000000
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => 0000000
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => 0000000
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => 0000000
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => 0000000
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => 0000000
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => 0000000
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => 0000000
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => 0000000
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => 0000000
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => 0000000
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => 0000000
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => 0000000
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => 0000000
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => 0000000
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => 0000000
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => 0000000
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => 0000000
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => 0000000
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => 0000000
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => 0000000
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => 0000000
[[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => 0000000
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => 0000000
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => 0000000
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => 0000000
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => 0000000
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => 0000000
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => 0000000
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => 0000000
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => 0000000
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => 0000000
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => 0000000
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => 0000000
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => 0000000
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => 0000000
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => 0000000
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => 0000000
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => 0000000
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => 0000000
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => 0000000
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => 0000000
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => 0000000
[[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => 0000000
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => 0000000
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => 0000000
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => 0000000
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => 0000000
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => 0000000
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => 0000000
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => 0000000
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => 0000000
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => 0000000
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => 0000000
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => 0000000
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => 0000000
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => 0000000
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => 0000000
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => 0000000
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => 0000000
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => 0000000
[[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => 0000000
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => 0000000
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => 0000000
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => 0000000
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => 0000000
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => 0000000
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => 0000000
[[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => 0000000
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => 0000000
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => 0000000
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => 0000000
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => 0000000
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => 0000000
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => 0000000
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => 0000000
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => 0000000
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => 0000000
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => 0000000
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => 0000000
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => 0000000
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => 0000000
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => 0000000
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => 0000000
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => 0000000
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => 0000000
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => 0000000
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => 0000000
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => 0000000
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => 0000000
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => 0000000
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => 0000000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => 0000000
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => 0000000
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => 0000000
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => 0000000
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => 0000000
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => 0000000
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => 0000000
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => 0000000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => 0000000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => 0000000
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => 0000000
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => 0000000
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => 0000000
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => 0000000
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => 0000000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => 0000000
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => 0000000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => 0000000
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => 0000000
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => 0000000
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => 0000000
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => 0000000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => 0000000
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => 0000000
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => 0000000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => 0000000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => 0000000
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => 0000000
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => 0000000
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => 0000000
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => 0000000
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => 0000000
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => 0000000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => 0000000
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => 0000000
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => 0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => 11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => 11111110
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => 11111100
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => 11111000
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => 11110000
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => 11100000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => 11000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => 00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => 111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => 111111110
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => 11111101
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => 111111100
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => 11111010
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => 111111000
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => 11110100
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => 111110000
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => 11101000
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => 111100000
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => 11010000
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => 111000000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => 10100000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => 110000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => 01000000
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 100000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => 000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => 11111100
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => 11100000
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => 11000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 00000000
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => 111110000
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => 00000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 000000000
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 010101010
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => 000000000
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 01010101010
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => 00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => 000000001
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,7,5,4,6,3,2,1,9] => 00000001
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,7,4,6,5,3,2,1,9] => 00000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,9,8,6,5,7,4,3,2] => 10000000
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => 00000011
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,9,8,6,7,5,4,3] => 01000000
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 010000000
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => 01111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => 00000000
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => 011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000000
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => 000000000
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => 00000000
[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => 101010100
[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => 10101010100
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => 000000000
[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => 100000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => 00111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => 00011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => 00001111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => 00000111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => 00000011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => 00000001
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => 00111111
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => 00000000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9,8,7,4,5,6,3,2,1] => 00000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => 00000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => 000000000
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => 00000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9,8,5,4,6,7,3,2,1] => 00000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9,8,7,5,4,6,3,2,1] => 00000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,9,8,7,5,6,4,3,2,1] => 000000000
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => 10111111
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => 101010101
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => 001010101
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => 10000001
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => 100000001
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => 00000000
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => 11111000
[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => 11110000
[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => 11100000
[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => 11000000
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => 10000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => 00000000
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,8,7,4,6,5,3,2,1] => 00000000
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9,8,4,6,5,7,3,2,1] => 00000000
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [9,8,3,6,5,4,7,2,1] => 00000000
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9,3,7,6,5,4,8,2,1] => 00000000
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9,2,7,6,5,4,3,8,1] => 00000000
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => 00000000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => 00000000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => 00000000
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [10,9,8,6,5,7,4,3,2,1] => 000000000
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => 000000000
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => 10000001
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9,4,5,6,7,8,3,2] => 10000000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => 00000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => 00000010
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => 0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => 001111111
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => 00011111
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9,8,4,5,3,7,6,2,1] => 00000000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => 100000001
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => 00100000
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => 00000000
[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => 10000010
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => 000000011
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => 00000000
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => 00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => 00011111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => 00000001
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => 000000111
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => 00000011
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => 000001111
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => 00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => 000011111
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => 000111111
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => 000000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1111111110
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => 00000000
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => 01000000
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => 00000000
[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => 00000000
[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => 00000000
[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => 00100000
[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => 1111111100
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => 000000010
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
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