Identifier
Mp00020:
Binary trees
—to Tamari-corresponding Dyck path⟶
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] =>
[.,[.,.]] => [1,1,0,0] => [2,1] => 0
[[.,.],.] => [1,0,1,0] => [1,2] => 1
[.,[.,[.,.]]] => [1,1,1,0,0,0] => [3,2,1] => 00
[.,[[.,.],.]] => [1,1,0,1,0,0] => [2,3,1] => 00
[[.,.],[.,.]] => [1,0,1,1,0,0] => [1,3,2] => 10
[[.,[.,.]],.] => [1,1,0,0,1,0] => [2,1,3] => 01
[[[.,.],.],.] => [1,0,1,0,1,0] => [1,2,3] => 11
[.,[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 000
[.,[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => 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
[.,[[[.,.],.],.]] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 000
[[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 100
[[.,.],[[.,.],.]] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 100
[[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 010
[[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 110
[[.,[.,[.,.]]],.] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 001
[[.,[[.,.],.]],.] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 001
[[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 101
[[[.,[.,.]],.],.] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 011
[[[[.,.],.],.],.] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 111
[.,[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0000
[.,[.,[.,[[.,.],.]]]] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => 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
[.,[.,[[[.,.],.],.]]] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => 0000
[.,[[.,.],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0000
[.,[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => 0000
[.,[[.,[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 0000
[.,[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => 0000
[.,[[.,[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0000
[.,[[.,[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => 0000
[.,[[[.,.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => 0000
[.,[[[.,[.,.]],.],.]] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 0000
[.,[[[[.,.],.],.],.]] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 0000
[[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000
[[.,.],[.,[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 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
[[.,.],[[[.,.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000
[[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100
[[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100
[[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1100
[[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1100
[[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010
[[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1010
[[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 0110
[[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1110
[[.,[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001
[[.,[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 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
[[.,[[[.,.],.],.]],.] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001
[[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1001
[[[.,.],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 1001
[[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 0101
[[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 1101
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0011
[[[.,[[.,.],.]],.],.] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 0011
[[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 1011
[[[[.,[.,.]],.],.],.] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 0111
[[[[[.,.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 1111
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 00000
[.,[.,[.,[.,[[.,.],.]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => 00000
[.,[.,[.,[[.,.],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [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
[.,[.,[.,[[[.,.],.],.]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => 00000
[.,[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => 00000
[.,[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => 00000
[.,[.,[[.,[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => 00000
[.,[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => 00000
[.,[.,[[.,[.,[.,.]]],.]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => 00000
[.,[.,[[.,[[.,.],.]],.]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => 00000
[.,[.,[[[.,.],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => 00000
[.,[.,[[[.,[.,.]],.],.]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => 00000
[.,[.,[[[[.,.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => 00000
[.,[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 00000
[.,[[.,.],[.,[[.,.],.]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => 00000
[.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [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
[.,[[.,.],[[[.,.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => 00000
[.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 00000
[.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => 00000
[.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 00000
[.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => 00000
[.,[[.,[.,[.,.]]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 00000
[.,[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => 00000
[.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 00000
[.,[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 00000
[.,[[[[.,.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => 00000
[.,[[.,[.,[.,[.,.]]]],.]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 00000
[.,[[.,[.,[[.,.],.]]],.]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => 00000
[.,[[.,[[.,.],[.,.]]],.]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [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
[.,[[.,[[[.,.],.],.]],.]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => 00000
[.,[[[.,.],[.,[.,.]]],.]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 00000
[.,[[[.,.],[[.,.],.]],.]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => 00000
[.,[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 00000
[.,[[[[.,.],.],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => 00000
>>> Load all 1518 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 00000
[.,[[[.,[[.,.],.]],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => 00000
[.,[[[[.,.],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => 00000
[.,[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 00000
[.,[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 00000
[[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 10000
[[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 10000
[[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [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
[[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 10000
[[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 10000
[[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 10000
[[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 10000
[[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 10000
[[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 10000
[[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 10000
[[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 10000
[[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 10000
[[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 10000
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 01000
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 01000
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [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
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 01000
[[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 11000
[[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 11000
[[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [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
[[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 11000
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 00100
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 00100
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 00100
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 00100
[[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 10100
[[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 10100
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 01100
[[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 01100
[[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 11100
[[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 11100
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 00010
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => 00010
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 00010
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 00010
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 00010
[[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 10010
[[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 10010
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 01010
[[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 11010
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 00110
[[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 00110
[[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 10110
[[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 01110
[[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 11110
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 00001
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 00001
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,1,0,1,1,0,0,0,0,1,0] => [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
[[.,[.,[[[.,.],.],.]]],.] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => 00001
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 00001
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => 00001
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 00001
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 00001
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 00001
[[.,[[.,[[.,.],.]],.]],.] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => 00001
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 00001
[[.,[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 00001
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 00001
[[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 10001
[[[.,.],[.,[[.,.],.]]],.] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => 10001
[[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [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
[[[.,.],[[[.,.],.],.]],.] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 10001
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 01001
[[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 01001
[[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 11001
[[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 11001
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 00101
[[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 00101
[[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 10101
[[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 01101
[[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 11101
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 00011
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => 00011
[[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 00011
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 00011
[[[.,[[[.,.],.],.]],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 00011
[[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 10011
[[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 10011
[[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 01011
[[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 11011
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 00111
[[[[.,[[.,.],.]],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 00111
[[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 10111
[[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 01111
[[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => 000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => 000000
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [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
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => 000000
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => 000000
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => 000000
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => 000000
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => 000000
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => 000000
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => 000000
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => 000000
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => 000000
[.,[.,[.,[[[[.,.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => 000000
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => 000000
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => 000000
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [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
[.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => 000000
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => 000000
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => 000000
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => 000000
[.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => 000000
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => 000000
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => 000000
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => 000000
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => 000000
[.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => 000000
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => 000000
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => 000000
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [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
[.,[.,[[.,[[[.,.],.],.]],.]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => 000000
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => 000000
[.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => 000000
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => 000000
[.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => 000000
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => 000000
[.,[.,[[[.,[[.,.],.]],.],.]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => 000000
[.,[.,[[[[.,.],[.,.]],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => 000000
[.,[.,[[[[.,[.,.]],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => 000000
[.,[.,[[[[[.,.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => 000000
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => 000000
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => 000000
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [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
[.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => 000000
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => 000000
[.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => 000000
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => 000000
[.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => 000000
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => 000000
[.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => 000000
[.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => 000000
[.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => 000000
[.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => 000000
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => 000000
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => 000000
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [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
[.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => 000000
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => 000000
[.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => 000000
[.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [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
[.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => 000000
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => 000000
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => 000000
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => 000000
[.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => 000000
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => 000000
[.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => 000000
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => 000000
[.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => 000000
[.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => 000000
[.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => 000000
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => 000000
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => 000000
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => 000000
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => 000000
[.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => 000000
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => 000000
[.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => 000000
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => 000000
[.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => 000000
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => 000000
[.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => 000000
[.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => 000000
[.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => 000000
[.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => 000000
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => 000000
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => 000000
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [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
[.,[[.,[.,[[[.,.],.],.]]],.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => 000000
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => 000000
[.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => 000000
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => 000000
[.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => 000000
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => 000000
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => 000000
[.,[[.,[[[.,.],[.,.]],.]],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => 000000
[.,[[.,[[[.,[.,.]],.],.]],.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => 000000
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => 000000
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => 000000
[.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => 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
[.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => 000000
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => 000000
[.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => 000000
[.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => 000000
[.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => 000000
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => 000000
[.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => 000000
[.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => 000000
[.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => 000000
[.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => 000000
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => 000000
[.,[[[.,[.,[[.,.],.]]],.],.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => 000000
[.,[[[.,[[.,.],[.,.]]],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => 000000
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => 000000
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => 000000
[.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => 000000
[.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => 000000
[.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => 000000
[.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => 000000
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => 000000
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => 000000
[.,[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => 000000
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => 000000
[.,[[[[[[.,.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 000000
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 100000
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 100000
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [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
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 100000
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 100000
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => 100000
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => 100000
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => 100000
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => 100000
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => 100000
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => 100000
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => 100000
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => 100000
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 100000
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => 100000
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [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
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => 100000
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 100000
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => 100000
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 100000
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => 100000
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => 100000
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => 100000
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => 100000
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => 100000
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => 100000
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => 100000
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => 100000
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [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
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => 100000
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 100000
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => 100000
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => 100000
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => 100000
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => 100000
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => 100000
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => 100000
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 100000
[[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 100000
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 010000
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => 010000
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [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
[[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => 010000
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => 010000
[[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => 010000
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => 010000
[[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => 010000
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => 010000
[[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => 010000
[[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => 010000
[[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => 010000
[[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => 010000
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 110000
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => 110000
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [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
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => 110000
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 110000
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => 110000
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => 110000
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => 110000
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 110000
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 110000
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => 110000
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 110000
[[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 110000
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => 001000
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => 001000
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [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
[[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => 001000
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => 001000
[[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => 001000
[[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [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
[[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => 001000
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 101000
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => 101000
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [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
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => 101000
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => 011000
[[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => 011000
[[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [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
[[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => 011000
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 111000
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => 111000
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [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
[[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 111000
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => 000100
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => 000100
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => 000100
[[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => 000100
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => 000100
[[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => 000100
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => 000100
[[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => 000100
[[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => 000100
[[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => 000100
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 100100
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => 100100
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => 100100
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => 100100
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => 010100
[[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => 010100
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => 110100
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => 110100
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => 001100
[[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => 001100
[[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => 001100
[[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => 001100
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => 101100
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => 101100
[[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => 011100
[[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => 011100
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 111100
[[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 111100
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 000010
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => 000010
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => 000010
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => 000010
[[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => 000010
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => 000010
[[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => 000010
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => 000010
[[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => 000010
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => 000010
[[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => 000010
[[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => 000010
[[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => 000010
[[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => 000010
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => 100010
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => 100010
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => 100010
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => 100010
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => 100010
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => 010010
[[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => 010010
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => 110010
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => 110010
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => 001010
[[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => 001010
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => 101010
[[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => 011010
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => 111010
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => 000110
[[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => 000110
[[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => 000110
[[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => 000110
[[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => 000110
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => 100110
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => 100110
[[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => 010110
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => 110110
[[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => 001110
[[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => 001110
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => 101110
[[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => 011110
[[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 111110
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 000001
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => 000001
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [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
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => 000001
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => 000001
[[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => 000001
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => 000001
[[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => 000001
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => 000001
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => 000001
[[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => 000001
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => 000001
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => 000001
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => 000001
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => 000001
[[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [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
[[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => 000001
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => 000001
[[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => 000001
[[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => 000001
[[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => 000001
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => 000001
[[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => 000001
[[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => 000001
[[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => 000001
[[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => 000001
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 000001
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => 000001
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [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
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => 000001
[[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => 000001
[[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => 000001
[[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => 000001
[[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => 000001
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => 000001
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => 000001
[[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => 000001
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => 000001
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => 000001
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => 100001
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => 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
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => 100001
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 100001
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => 100001
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => 100001
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => 100001
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => 100001
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => 100001
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => 100001
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => 100001
[[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => 100001
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => 010001
[[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => 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
[[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => 010001
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 110001
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => 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
[[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => 110001
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => 001001
[[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => 001001
[[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => 001001
[[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => 001001
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => 101001
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => 101001
[[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => 011001
[[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => 011001
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => 111001
[[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => 111001
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => 000101
[[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => 000101
[[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => 000101
[[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => 000101
[[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => 000101
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => 100101
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => 100101
[[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => 010101
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => 110101
[[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => 001101
[[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => 001101
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => 101101
[[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => 011101
[[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 111101
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => 000011
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => 000011
[[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => 000011
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => 000011
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => 000011
[[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => 000011
[[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => 000011
[[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => 000011
[[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => 000011
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => 000011
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => 000011
[[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => 000011
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => 000011
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => 000011
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => 100011
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => 100011
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => 100011
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => 100011
[[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => 100011
[[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => 010011
[[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => 010011
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => 110011
[[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => 110011
[[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => 001011
[[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => 001011
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => 101011
[[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => 011011
[[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => 111011
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => 000111
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => 000111
[[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => 000111
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => 000111
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => 000111
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => 100111
[[[[[.,.],[[.,.],.]],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => 100111
[[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => 010111
[[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => 110111
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => 001111
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => 001111
[[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 101111
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 011111
[[[[[[[.,.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [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
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => 0000000
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [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
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => 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
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => 0000000
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => 0000000
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => 0000000
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => 0000000
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => 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
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => 0000000
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => 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
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [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
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => 0000000
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => 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
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => 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
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => 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
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => 0000000
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => 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
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => 0000000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => 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
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => 0000000
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [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
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => 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
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => 0000000
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => 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
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => 0000000
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => 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
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => 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
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => 0000000
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => 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
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => 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
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => 0000000
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => 0000000
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => 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
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [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
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => 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
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => 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
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => 0000000
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => 0000000
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => 0000000
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => 0000000
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => 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
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => 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
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => 0000000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => 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
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => 0000000
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => 0000000
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [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
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => 0000000
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => 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
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => 0000000
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => 0000000
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => 0000000
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => 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
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => 0000000
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => 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
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => 0000000
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => 0000000
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => 0000000
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => 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
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => 0000000
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => 0000000
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => 0000000
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => 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
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => 0000000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => 0000000
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => 0000000
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => 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
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => 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
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => 0000000
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => 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
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => 0000000
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => 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
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => 0000000
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => 0000000
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => 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
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => 0000000
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => 0000000
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => 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
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => 0000000
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => 0000000
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => 0000000
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => 0000000
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => 0000000
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => 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
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => 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
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => 0000000
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => 0000000
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => 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
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => 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
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => 0000000
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => 0000000
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => 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
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => 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
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => 0000000
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [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
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => 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
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => 0000000
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => 0000000
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => 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
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => 0000000
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => 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
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => 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
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => 0000000
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => 0000000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => 0000000
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => 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
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => 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
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => 0000000
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => 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
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => 0000000
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [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
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => 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
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => 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
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => 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
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => 0000000
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => 0000000
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => 0000000
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => 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
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => 0000000
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => 0000000
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => 0000000
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => 0000000
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => 0000000
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => 0000000
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => 0000000
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => 0000000
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => 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
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => 0000000
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => 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
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => 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
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => 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
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => 0000000
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => 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
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => 0000000
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => 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
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => 0000000
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => 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
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => 0000000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => 0000000
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => 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
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => 0000000
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 0000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [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
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 1000000
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [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
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => 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
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => 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
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => 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
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => 1000000
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => 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
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => 1000000
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => 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
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => 1000000
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => 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
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => 1000000
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => 1000000
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [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
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => 1000000
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => 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
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => 1000000
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => 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
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => 1000000
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => 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
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => 1000000
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [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
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => 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
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => 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
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => 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
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => 1000000
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [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
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => 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
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => 1000000
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => 1000000
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => 1000000
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => 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
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => 1000000
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [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
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => 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
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => 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
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => 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
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => 1000000
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => 1000000
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => 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
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => 1000000
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => 1000000
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => 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
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => 1000000
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => 1000000
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => 1000000
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => 1000000
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [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
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 0100000
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => 0100000
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [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
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => 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
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => 0100000
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => 0100000
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => 0100000
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => 0100000
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => 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
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => 0100000
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => 0100000
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => 0100000
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => 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
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => 0100000
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => 0100000
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => 0100000
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => 0100000
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => 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
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => 0100000
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => 0100000
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [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
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => 1100000
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => 1100000
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => 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
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [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
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => 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
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => 1100000
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => 1100000
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => 1100000
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => 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
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => 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
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => 1100000
[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => 1100000
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => 1100000
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => 1100000
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => 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
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => 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
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => 1100000
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => 1100000
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => 1100000
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [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
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 0010000
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => 0010000
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [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
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => 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
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => 0010000
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => 0010000
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => 0010000
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => 0010000
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => 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
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => 0010000
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => 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
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => 0010000
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => 0010000
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => 0010000
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [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
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => 1010000
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => 1010000
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [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
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [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
[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => 1010000
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => 1010000
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => 1010000
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [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
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => 0110000
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [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
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => 0110000
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [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
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => 1110000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => 1110000
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [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
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => 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
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => 1110000
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => 1110000
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => 1110000
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => 1110000
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => 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
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => 1110000
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 1110000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [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
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => 0001000
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [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
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => 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
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => 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
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => 0001000
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => 0001000
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => 0001000
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [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
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => 0001000
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => 0001000
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [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
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => 1001000
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [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
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => 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
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => 1001000
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => 1001000
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [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
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => 0101000
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [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
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => 1101000
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => 1101000
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => 1101000
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [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
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => 0011000
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => 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
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => 0011000
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [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
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => 1011000
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => 1011000
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => 1011000
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [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
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => 0111000
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => 0111000
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [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
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => 1111000
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [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
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => 1111000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [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
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => 0000100
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => 0000100
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => 0000100
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [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
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => 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
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => 0000100
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [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
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => 0000100
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => 0000100
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => 0000100
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [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
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => 0000100
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => 0000100
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [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
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => 0000100
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => 0000100
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => 0000100
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => 0000100
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [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
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => 1000100
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => 1000100
[[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => 1000100
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [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
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => 1000100
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => 1000100
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [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
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => 0100100
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [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
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => 1100100
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => 1100100
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => 1100100
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [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
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => 1010100
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [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
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => 0110100
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [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
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => 1110100
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [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
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => 0001100
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [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
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => 0001100
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => 0001100
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [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
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => 1001100
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [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
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => 0101100
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => 0101100
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [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
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => 1101100
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [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
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => 0011100
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [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
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => 1011100
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => 1011100
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [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
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => 0111100
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [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
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => 1111100
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [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
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => 0000010
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [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
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => 0000010
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [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
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => 0000010
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [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
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => 0000010
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [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
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => 0000010
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => 0000010
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => 0000010
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => 0000010
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => 0000010
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [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
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => 0000010
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [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
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => 0000010
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [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
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => 0000010
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [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
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => 1000010
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => 1000010
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => 1000010
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => 1000010
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => 1000010
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [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
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => 0100010
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => 0100010
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [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
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => 1100010
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => 0010010
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => 0010010
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [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
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => 1010010
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [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
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => 0110010
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [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
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => 1110010
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [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
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => 0001010
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [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
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => 1001010
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 0101010
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => 1101010
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => 0011010
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => 1011010
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => 0111010
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => 1111010
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => 0000110
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => 0000110
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [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
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => 0000110
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [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
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => 0000110
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => 0000110
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => 0000110
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => 0000110
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => 0000110
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [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
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => 0100110
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => 1100110
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => 0110110
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => 1110110
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => 0001110
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => 0001110
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [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
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => 1001110
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [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
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => 1101110
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => 0011110
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => 0011110
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [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
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 0111110
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1111110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 0000001
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => 0000001
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [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
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => 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
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => 0000001
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => 0000001
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => 0000001
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => 0000001
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => 0000001
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => 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
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => 0000001
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => 0000001
[[.,[.,[[[.,.],.],[[.,.],.]]]],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => 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
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => 0000001
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => 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
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => 0000001
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [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
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => 0000001
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => 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
[[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => 0000001
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => 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
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => 0000001
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => 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
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => 0000001
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [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
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => 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
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => 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
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => 0000001
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => 0000001
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => 0000001
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [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
[[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => 0000001
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => 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
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => 0000001
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => 0000001
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => 0000001
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => 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
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => 0000001
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => 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
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => 0000001
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => 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
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => 0000001
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => 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
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => 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
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => 0000001
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => 0000001
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [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
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => 1000001
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => 1000001
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => 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
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => 1000001
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => 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
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => 1000001
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => 1000001
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => 1000001
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [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
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => 1000001
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [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
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => 0100001
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => 0100001
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [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
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => 1100001
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => 1100001
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [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
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => 0010001
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => 0010001
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [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
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => 0010001
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => 0010001
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [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
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => 1110001
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => 1110001
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [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
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => 1110001
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [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
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => 0001001
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [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
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => 0001001
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => 0001001
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [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
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => 1001001
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [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
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => 0101001
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => 1101001
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => 0011001
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => 1011001
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => 1111001
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => 1111001
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [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
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => 0000101
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => 0000101
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => 0000101
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [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
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => 0000101
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => 0000101
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [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
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => 1000101
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => 1000101
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [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
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => 1100101
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => 0010101
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => 0010101
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [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
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 1110101
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [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
[[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => 0001101
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [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
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => 1101101
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [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
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => 0011101
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [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
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => 0111101
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 1111101
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => 0000011
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => 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
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => 0000011
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [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
[[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => 0000011
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => 0000011
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => 0000011
[[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [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
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => 0000011
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => 0000011
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => 0000011
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [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
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => 0000011
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => 0000011
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => 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
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => 0000011
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => 0000011
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => 0000011
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [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
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => 1000011
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [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
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => 1000011
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => 1000011
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [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
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => 1000011
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [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
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => 0100011
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => 1100011
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => 1100011
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => 1100011
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [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
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => 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
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => 0010011
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [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
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => 1110011
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => 1110011
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [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
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => 0001011
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [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
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => 0001011
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => 0001011
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => 0101011
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [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
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => 1011011
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [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
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => 1111011
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => 0000111
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => 0000111
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [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
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => 0000111
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => 0000111
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [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
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => 0000111
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [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
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => 0000111
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => 0000111
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => 0000111
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [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
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => 0000111
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => 0000111
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [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
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => 1000111
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [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
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => 0100111
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [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
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => 0010111
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => 0010111
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [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
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => 0110111
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => 1110111
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => 0001111
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => 0001111
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [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
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => 0001111
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => 0001111
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [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
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => 1001111
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [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
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => 1101111
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => 0011111
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => 0011111
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [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
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => 0111111
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 1111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => 00000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => 00000000
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9,8,7,4,5,6,3,2,1] => 00000000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => 00000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 00000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => 11111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [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
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,9,8,7,5,6,4,3,2,1] => 000000000
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,8,7,4,6,5,3,2,1] => 00000000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => 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
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => 10000000
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [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
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => 111111111
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => 00000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => 00000001
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [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
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => 000000001
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => 000000000
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,9,8,1,10] => 000000001
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [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
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 01010101010
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => 11111110
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => 111111110
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => 10111110
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => 00111110
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => 00000000
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => 10000000
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => 100000000
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [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
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => 00000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [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
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => 0000000001
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,7,5,6,4,3,2,1,10] => 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
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => 000000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => 01000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => 00100000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => 00010000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => 00001000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => 00000100
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => 00000010
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [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
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => 00000011
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [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
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => 00111111
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => 01111111
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => 000000011
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => 000000111
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => 000001111
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => 000011111
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => 000111111
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => 10011111
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [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
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => 10111111
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => 011111111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => 00000000
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => 00000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => 000000000
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => 01011111
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => 00101111
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => 00000101
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [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
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => 00111111
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => 00011111
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => 11011111
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => 11101111
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => 11110111
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => 11111011
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [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
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => 101111111
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => 110111111
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => 111011111
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => 111101111
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => 111110111
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => 111111011
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => 111111101
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => 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
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => 10000010
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => 00000100
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => 1111111111
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [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
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => 10001111
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => 11001111
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => 01001111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => 000000000
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [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
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => 10000001
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => 11111010
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => 111111010
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,6,7,5,4,3,2,1] => 0000000000
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,7,6,4,5,3,2,9,1] => 00000000
[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => 00000000
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => 00001001
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => 000000101
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => 10011111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,5,4,3,2,1,9,10,8] => 000000100
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ 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.
searching the database
Sorry, this map was not found in the database.