Identifier
Mp00018:
Binary trees
—left border symmetry⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
[.,.] => [.,.] => [1] =>
[.,[.,.]] => [.,[.,.]] => [2,1] => 0
[[.,.],.] => [[.,.],.] => [1,2] => 1
[.,[.,[.,.]]] => [.,[.,[.,.]]] => [3,2,1] => 00
[.,[[.,.],.]] => [.,[[.,.],.]] => [2,3,1] => 00
[[.,.],[.,.]] => [[.,[.,.]],.] => [2,1,3] => 01
[[.,[.,.]],.] => [[.,.],[.,.]] => [1,3,2] => 10
[[[.,.],.],.] => [[[.,.],.],.] => [1,2,3] => 11
[.,[.,[.,[.,.]]]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 000
[.,[.,[[.,.],.]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 000
[.,[[.,.],[.,.]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 000
[.,[[.,[.,.]],.]] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 000
[.,[[[.,.],.],.]] => [.,[[[.,.],.],.]] => [2,3,4,1] => 000
[[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 001
[[.,.],[[.,.],.]] => [[.,[[.,.],.]],.] => [2,3,1,4] => 001
[[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 010
[[[.,.],.],[.,.]] => [[[.,[.,.]],.],.] => [2,1,3,4] => 011
[[.,[.,[.,.]]],.] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 100
[[.,[[.,.],.]],.] => [[.,.],[[.,.],.]] => [1,3,4,2] => 100
[[[.,.],[.,.]],.] => [[[.,.],[.,.]],.] => [1,3,2,4] => 101
[[[.,[.,.]],.],.] => [[[.,.],.],[.,.]] => [1,2,4,3] => 110
[[[[.,.],.],.],.] => [[[[.,.],.],.],.] => [1,2,3,4] => 111
[.,[.,[.,[.,[.,.]]]]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 0000
[.,[.,[.,[[.,.],.]]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 0000
[.,[.,[[.,.],[.,.]]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 0000
[.,[.,[[.,[.,.]],.]]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 0000
[.,[.,[[[.,.],.],.]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 0000
[.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 0000
[.,[[.,.],[[.,.],.]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 0000
[.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 0000
[.,[[[.,.],.],[.,.]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 0000
[.,[[.,[.,[.,.]]],.]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 0000
[.,[[.,[[.,.],.]],.]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 0000
[.,[[[.,.],[.,.]],.]] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 0000
[.,[[[.,[.,.]],.],.]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 0000
[.,[[[[.,.],.],.],.]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 0000
[[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 0001
[[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 0001
[[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 0001
[[.,.],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 0001
[[.,.],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 0001
[[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 0010
[[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 0010
[[[.,.],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 0011
[[[.,.],.],[[.,.],.]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 0011
[[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 0100
[[.,[[.,.],.]],[.,.]] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 0100
[[[.,.],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 0101
[[[.,[.,.]],.],[.,.]] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 0110
[[[[.,.],.],.],[.,.]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 0111
[[.,[.,[.,[.,.]]]],.] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 1000
[[.,[.,[[.,.],.]]],.] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 1000
[[.,[[.,.],[.,.]]],.] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 1000
[[.,[[.,[.,.]],.]],.] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 1000
[[.,[[[.,.],.],.]],.] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 1000
[[[.,.],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 1001
[[[.,.],[[.,.],.]],.] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 1001
[[[.,[.,.]],[.,.]],.] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 1010
[[[[.,.],.],[.,.]],.] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 1011
[[[.,[.,[.,.]]],.],.] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 1100
[[[.,[[.,.],.]],.],.] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 1100
[[[[.,.],[.,.]],.],.] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 1101
[[[[.,[.,.]],.],.],.] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 1110
[[[[[.,.],.],.],.],.] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 1111
[.,[.,[.,[.,[.,[.,.]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 00000
[.,[.,[.,[.,[[.,.],.]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 00000
[.,[.,[.,[[.,.],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 00000
[.,[.,[.,[[.,[.,.]],.]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 00000
[.,[.,[.,[[[.,.],.],.]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 00000
[.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 00000
[.,[.,[[.,.],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 00000
[.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 00000
[.,[.,[[[.,.],.],[.,.]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 00000
[.,[.,[[.,[.,[.,.]]],.]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 00000
[.,[.,[[.,[[.,.],.]],.]]] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 00000
[.,[.,[[[.,.],[.,.]],.]]] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 00000
[.,[.,[[[.,[.,.]],.],.]]] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 00000
[.,[.,[[[[.,.],.],.],.]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 00000
[.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 00000
[.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 00000
[.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 00000
[.,[[.,.],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 00000
[.,[[.,.],[[[.,.],.],.]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 00000
[.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 00000
[.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 00000
[.,[[[.,.],.],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 00000
[.,[[[.,.],.],[[.,.],.]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 00000
[.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 00000
[.,[[.,[[.,.],.]],[.,.]]] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 00000
[.,[[[.,.],[.,.]],[.,.]]] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 00000
[.,[[[.,[.,.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 00000
[.,[[[[.,.],.],.],[.,.]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 00000
[.,[[.,[.,[.,[.,.]]]],.]] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 00000
[.,[[.,[.,[[.,.],.]]],.]] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 00000
[.,[[.,[[.,.],[.,.]]],.]] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 00000
[.,[[.,[[.,[.,.]],.]],.]] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 00000
[.,[[.,[[[.,.],.],.]],.]] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 00000
[.,[[[.,.],[.,[.,.]]],.]] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 00000
[.,[[[.,.],[[.,.],.]],.]] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 00000
[.,[[[.,[.,.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 00000
[.,[[[[.,.],.],[.,.]],.]] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 00000
>>> Load all 1653 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 00000
[.,[[[.,[[.,.],.]],.],.]] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 00000
[.,[[[[.,.],[.,.]],.],.]] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 00000
[.,[[[[.,[.,.]],.],.],.]] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 00000
[.,[[[[[.,.],.],.],.],.]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 00000
[[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 00001
[[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 00001
[[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 00001
[[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 00001
[[.,.],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 00001
[[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 00001
[[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 00001
[[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 00001
[[.,.],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 00001
[[.,.],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 00001
[[.,.],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 00001
[[.,.],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 00001
[[.,.],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 00001
[[.,.],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 00001
[[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 00010
[[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 00010
[[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 00010
[[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 00010
[[.,[.,.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 00010
[[[.,.],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 00011
[[[.,.],.],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 00011
[[[.,.],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 00011
[[[.,.],.],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 00011
[[[.,.],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 00011
[[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 00100
[[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 00100
[[.,[[.,.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 00100
[[.,[[.,.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 00100
[[[.,.],[.,.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 00101
[[[.,.],[.,.]],[[.,.],.]] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 00101
[[[.,[.,.]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 00110
[[[.,[.,.]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 00110
[[[[.,.],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 00111
[[[[.,.],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 00111
[[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 01000
[[.,[.,[[.,.],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 01000
[[.,[[.,.],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 01000
[[.,[[.,[.,.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 01000
[[.,[[[.,.],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 01000
[[[.,.],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 01001
[[[.,.],[[.,.],.]],[.,.]] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 01001
[[[.,[.,.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 01010
[[[[.,.],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 01011
[[[.,[.,[.,.]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 01100
[[[.,[[.,.],.]],.],[.,.]] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 01100
[[[[.,.],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 01101
[[[[.,[.,.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 01110
[[[[[.,.],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 01111
[[.,[.,[.,[.,[.,.]]]]],.] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 10000
[[.,[.,[.,[[.,.],.]]]],.] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 10000
[[.,[.,[[.,.],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 10000
[[.,[.,[[.,[.,.]],.]]],.] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 10000
[[.,[.,[[[.,.],.],.]]],.] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 10000
[[.,[[.,.],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 10000
[[.,[[.,.],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 10000
[[.,[[.,[.,.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 10000
[[.,[[[.,.],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 10000
[[.,[[.,[.,[.,.]]],.]],.] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 10000
[[.,[[.,[[.,.],.]],.]],.] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 10000
[[.,[[[.,.],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 10000
[[.,[[[.,[.,.]],.],.]],.] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 10000
[[.,[[[[.,.],.],.],.]],.] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 10000
[[[.,.],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 10001
[[[.,.],[.,[[.,.],.]]],.] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 10001
[[[.,.],[[.,.],[.,.]]],.] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 10001
[[[.,.],[[.,[.,.]],.]],.] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 10001
[[[.,.],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 10001
[[[.,[.,.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 10010
[[[.,[.,.]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 10010
[[[[.,.],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 10011
[[[[.,.],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 10011
[[[.,[.,[.,.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 10100
[[[.,[[.,.],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 10100
[[[[.,.],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 10101
[[[[.,[.,.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 10110
[[[[[.,.],.],.],[.,.]],.] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 10111
[[[.,[.,[.,[.,.]]]],.],.] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 11000
[[[.,[.,[[.,.],.]]],.],.] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 11000
[[[.,[[.,.],[.,.]]],.],.] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 11000
[[[.,[[.,[.,.]],.]],.],.] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 11000
[[[.,[[[.,.],.],.]],.],.] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 11000
[[[[.,.],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 11001
[[[[.,.],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 11001
[[[[.,[.,.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 11010
[[[[[.,.],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 11011
[[[[.,[.,[.,.]]],.],.],.] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 11100
[[[[.,[[.,.],.]],.],.],.] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 11100
[[[[[.,.],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 11101
[[[[[.,[.,.]],.],.],.],.] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 11110
[[[[[[.,.],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => 000000
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => 000000
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => 000000
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => 000000
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => 000000
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => 000000
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => 000000
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => 000000
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => 000000
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => 000000
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => 000000
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => 000000
[.,[.,[.,[[[[.,.],.],.],.]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => 000000
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => 000000
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => 000000
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => 000000
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => 000000
[.,[.,[[.,.],[[[.,.],.],.]]]] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => 000000
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => 000000
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => 000000
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => 000000
[.,[.,[[[.,.],.],[[.,.],.]]]] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => 000000
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => 000000
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => 000000
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => 000000
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => 000000
[.,[.,[[[[.,.],.],.],[.,.]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => 000000
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => 000000
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => 000000
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => 000000
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => 000000
[.,[.,[[.,[[[.,.],.],.]],.]]] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => 000000
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => 000000
[.,[.,[[[.,.],[[.,.],.]],.]]] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => 000000
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => 000000
[.,[.,[[[[.,.],.],[.,.]],.]]] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => 000000
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => 000000
[.,[.,[[[.,[[.,.],.]],.],.]]] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => 000000
[.,[.,[[[[.,.],[.,.]],.],.]]] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => 000000
[.,[.,[[[[.,[.,.]],.],.],.]]] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => 000000
[.,[.,[[[[[.,.],.],.],.],.]]] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => 000000
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => 000000
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => 000000
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => 000000
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => 000000
[.,[[.,.],[.,[[[.,.],.],.]]]] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => 000000
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => 000000
[.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => 000000
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => 000000
[.,[[.,.],[[[.,.],.],[.,.]]]] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => 000000
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => 000000
[.,[[.,.],[[.,[[.,.],.]],.]]] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => 000000
[.,[[.,.],[[[.,.],[.,.]],.]]] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => 000000
[.,[[.,.],[[[.,[.,.]],.],.]]] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => 000000
[.,[[.,.],[[[[.,.],.],.],.]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 000000
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => 000000
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => 000000
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => 000000
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => 000000
[.,[[.,[.,.]],[[[.,.],.],.]]] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => 000000
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => 000000
[.,[[[.,.],.],[.,[[.,.],.]]]] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => 000000
[.,[[[.,.],.],[[.,.],[.,.]]]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 000000
[.,[[[.,.],.],[[.,[.,.]],.]]] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => 000000
[.,[[[.,.],.],[[[.,.],.],.]]] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 000000
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => 000000
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => 000000
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => 000000
[.,[[.,[[.,.],.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => 000000
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => 000000
[.,[[[.,.],[.,.]],[[.,.],.]]] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => 000000
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => 000000
[.,[[[.,[.,.]],.],[[.,.],.]]] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => 000000
[.,[[[[.,.],.],.],[.,[.,.]]]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 000000
[.,[[[[.,.],.],.],[[.,.],.]]] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 000000
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => 000000
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => 000000
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => 000000
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => 000000
[.,[[.,[[[.,.],.],.]],[.,.]]] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => 000000
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => 000000
[.,[[[.,.],[[.,.],.]],[.,.]]] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => 000000
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => 000000
[.,[[[[.,.],.],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => 000000
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => 000000
[.,[[[.,[[.,.],.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => 000000
[.,[[[[.,.],[.,.]],.],[.,.]]] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => 000000
[.,[[[[.,[.,.]],.],.],[.,.]]] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => 000000
[.,[[[[[.,.],.],.],.],[.,.]]] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 000000
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => 000000
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => 000000
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => 000000
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => 000000
[.,[[.,[.,[[[.,.],.],.]]],.]] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => 000000
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => 000000
[.,[[.,[[.,.],[[.,.],.]]],.]] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => 000000
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => 000000
[.,[[.,[[[.,.],.],[.,.]]],.]] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => 000000
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => 000000
[.,[[.,[[.,[[.,.],.]],.]],.]] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => 000000
[.,[[.,[[[.,.],[.,.]],.]],.]] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => 000000
[.,[[.,[[[.,[.,.]],.],.]],.]] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => 000000
[.,[[.,[[[[.,.],.],.],.]],.]] => [.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => 000000
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => 000000
[.,[[[.,.],[.,[[.,.],.]]],.]] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => 000000
[.,[[[.,.],[[.,.],[.,.]]],.]] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => 000000
[.,[[[.,.],[[.,[.,.]],.]],.]] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => 000000
[.,[[[.,.],[[[.,.],.],.]],.]] => [.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => 000000
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => 000000
[.,[[[.,[.,.]],[[.,.],.]],.]] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => 000000
[.,[[[[.,.],.],[.,[.,.]]],.]] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => 000000
[.,[[[[.,.],.],[[.,.],.]],.]] => [.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => 000000
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => 000000
[.,[[[.,[[.,.],.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => 000000
[.,[[[[.,.],[.,.]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => 000000
[.,[[[[.,[.,.]],.],[.,.]],.]] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => 000000
[.,[[[[[.,.],.],.],[.,.]],.]] => [.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => 000000
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => 000000
[.,[[[.,[.,[[.,.],.]]],.],.]] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => 000000
[.,[[[.,[[.,.],[.,.]]],.],.]] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => 000000
[.,[[[.,[[.,[.,.]],.]],.],.]] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => 000000
[.,[[[.,[[[.,.],.],.]],.],.]] => [.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => 000000
[.,[[[[.,.],[.,[.,.]]],.],.]] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => 000000
[.,[[[[.,.],[[.,.],.]],.],.]] => [.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => 000000
[.,[[[[.,[.,.]],[.,.]],.],.]] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => 000000
[.,[[[[[.,.],.],[.,.]],.],.]] => [.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => 000000
[.,[[[[.,[.,[.,.]]],.],.],.]] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => 000000
[.,[[[[.,[[.,.],.]],.],.],.]] => [.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => 000000
[.,[[[[[.,.],[.,.]],.],.],.]] => [.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => 000000
[.,[[[[[.,[.,.]],.],.],.],.]] => [.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => 000000
[.,[[[[[[.,.],.],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 000000
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 000001
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 000001
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 000001
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 000001
[[.,.],[.,[.,[[[.,.],.],.]]]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 000001
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 000001
[[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 000001
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 000001
[[.,.],[.,[[[.,.],.],[.,.]]]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => 000001
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 000001
[[.,.],[.,[[.,[[.,.],.]],.]]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 000001
[[.,.],[.,[[[.,.],[.,.]],.]]] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => 000001
[[.,.],[.,[[[.,[.,.]],.],.]]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => 000001
[[.,.],[.,[[[[.,.],.],.],.]]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => 000001
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 000001
[[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => 000001
[[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => 000001
[[.,.],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => 000001
[[.,.],[[.,.],[[[.,.],.],.]]] => [[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => 000001
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => 000001
[[.,.],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => 000001
[[.,.],[[[.,.],.],[.,[.,.]]]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => 000001
[[.,.],[[[.,.],.],[[.,.],.]]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => 000001
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => 000001
[[.,.],[[.,[[.,.],.]],[.,.]]] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => 000001
[[.,.],[[[.,.],[.,.]],[.,.]]] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => 000001
[[.,.],[[[.,[.,.]],.],[.,.]]] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => 000001
[[.,.],[[[[.,.],.],.],[.,.]]] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => 000001
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 000001
[[.,.],[[.,[.,[[.,.],.]]],.]] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => 000001
[[.,.],[[.,[[.,.],[.,.]]],.]] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => 000001
[[.,.],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => 000001
[[.,.],[[.,[[[.,.],.],.]],.]] => [[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => 000001
[[.,.],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => 000001
[[.,.],[[[.,.],[[.,.],.]],.]] => [[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => 000001
[[.,.],[[[.,[.,.]],[.,.]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => 000001
[[.,.],[[[[.,.],.],[.,.]],.]] => [[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => 000001
[[.,.],[[[.,[.,[.,.]]],.],.]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => 000001
[[.,.],[[[.,[[.,.],.]],.],.]] => [[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => 000001
[[.,.],[[[[.,.],[.,.]],.],.]] => [[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => 000001
[[.,.],[[[[.,[.,.]],.],.],.]] => [[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => 000001
[[.,.],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 000001
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => 000010
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => 000010
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => 000010
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => 000010
[[.,[.,.]],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => 000010
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => 000010
[[.,[.,.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => 000010
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => 000010
[[.,[.,.]],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => 000010
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => 000010
[[.,[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => 000010
[[.,[.,.]],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => 000010
[[.,[.,.]],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => 000010
[[.,[.,.]],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => 000010
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 000011
[[[.,.],.],[.,[.,[[.,.],.]]]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => 000011
[[[.,.],.],[.,[[.,.],[.,.]]]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => 000011
[[[.,.],.],[.,[[.,[.,.]],.]]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => 000011
[[[.,.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => 000011
[[[.,.],.],[[.,.],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => 000011
[[[.,.],.],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => 000011
[[[.,.],.],[[.,[.,.]],[.,.]]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => 000011
[[[.,.],.],[[[.,.],.],[.,.]]] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => 000011
[[[.,.],.],[[.,[.,[.,.]]],.]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => 000011
[[[.,.],.],[[.,[[.,.],.]],.]] => [[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => 000011
[[[.,.],.],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => 000011
[[[.,.],.],[[[.,[.,.]],.],.]] => [[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => 000011
[[[.,.],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 000011
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => 000100
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => 000100
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => 000100
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => 000100
[[.,[.,[.,.]]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => 000100
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => 000100
[[.,[[.,.],.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => 000100
[[.,[[.,.],.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => 000100
[[.,[[.,.],.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => 000100
[[.,[[.,.],.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => 000100
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => 000101
[[[.,.],[.,.]],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => 000101
[[[.,.],[.,.]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => 000101
[[[.,.],[.,.]],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => 000101
[[[.,.],[.,.]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => 000101
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => 000110
[[[.,[.,.]],.],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => 000110
[[[.,[.,.]],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => 000110
[[[.,[.,.]],.],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => 000110
[[[.,[.,.]],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => 000110
[[[[.,.],.],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 000111
[[[[.,.],.],.],[.,[[.,.],.]]] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => 000111
[[[[.,.],.],.],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => 000111
[[[[.,.],.],.],[[.,[.,.]],.]] => [[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => 000111
[[[[.,.],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 000111
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => 001000
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => 001000
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => 001000
[[.,[.,[[.,.],.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => 001000
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => 001000
[[.,[[.,.],[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => 001000
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => 001000
[[.,[[.,[.,.]],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => 001000
[[.,[[[.,.],.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => 001000
[[.,[[[.,.],.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => 001000
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => 001001
[[[.,.],[.,[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => 001001
[[[.,.],[[.,.],.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => 001001
[[[.,.],[[.,.],.]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => 001001
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => 001010
[[[.,[.,.]],[.,.]],[[.,.],.]] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => 001010
[[[[.,.],.],[.,.]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => 001011
[[[[.,.],.],[.,.]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => 001011
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => 001100
[[[.,[.,[.,.]]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => 001100
[[[.,[[.,.],.]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => 001100
[[[.,[[.,.],.]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => 001100
[[[[.,.],[.,.]],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => 001101
[[[[.,.],[.,.]],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => 001101
[[[[.,[.,.]],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => 001110
[[[[.,[.,.]],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => 001110
[[[[[.,.],.],.],.],[.,[.,.]]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 001111
[[[[[.,.],.],.],.],[[.,.],.]] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 001111
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 010000
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => 010000
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => 010000
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => 010000
[[.,[.,[[[.,.],.],.]]],[.,.]] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => 010000
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => 010000
[[.,[[.,.],[[.,.],.]]],[.,.]] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => 010000
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => 010000
[[.,[[[.,.],.],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => 010000
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => 010000
[[.,[[.,[[.,.],.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => 010000
[[.,[[[.,.],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => 010000
[[.,[[[.,[.,.]],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => 010000
[[.,[[[[.,.],.],.],.]],[.,.]] => [[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => 010000
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => 010001
[[[.,.],[.,[[.,.],.]]],[.,.]] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => 010001
[[[.,.],[[.,.],[.,.]]],[.,.]] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => 010001
[[[.,.],[[.,[.,.]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => 010001
[[[.,.],[[[.,.],.],.]],[.,.]] => [[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => 010001
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => 010010
[[[.,[.,.]],[[.,.],.]],[.,.]] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => 010010
[[[[.,.],.],[.,[.,.]]],[.,.]] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => 010011
[[[[.,.],.],[[.,.],.]],[.,.]] => [[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => 010011
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => 010100
[[[.,[[.,.],.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => 010100
[[[[.,.],[.,.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => 010101
[[[[.,[.,.]],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => 010110
[[[[[.,.],.],.],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => 010111
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => 011000
[[[.,[.,[[.,.],.]]],.],[.,.]] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => 011000
[[[.,[[.,.],[.,.]]],.],[.,.]] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => 011000
[[[.,[[.,[.,.]],.]],.],[.,.]] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => 011000
[[[.,[[[.,.],.],.]],.],[.,.]] => [[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => 011000
[[[[.,.],[.,[.,.]]],.],[.,.]] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => 011001
[[[[.,.],[[.,.],.]],.],[.,.]] => [[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => 011001
[[[[.,[.,.]],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => 011010
[[[[[.,.],.],[.,.]],.],[.,.]] => [[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => 011011
[[[[.,[.,[.,.]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => 011100
[[[[.,[[.,.],.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => 011100
[[[[[.,.],[.,.]],.],.],[.,.]] => [[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => 011101
[[[[[.,[.,.]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => 011110
[[[[[[.,.],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 011111
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 100000
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 100000
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 100000
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 100000
[[.,[.,[.,[[[.,.],.],.]]]],.] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 100000
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 100000
[[.,[.,[[.,.],[[.,.],.]]]],.] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 100000
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 100000
[[.,[.,[[[.,.],.],[.,.]]]],.] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => 100000
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 100000
[[.,[.,[[.,[[.,.],.]],.]]],.] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 100000
[[.,[.,[[[.,.],[.,.]],.]]],.] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => 100000
[[.,[.,[[[.,[.,.]],.],.]]],.] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => 100000
[[.,[.,[[[[.,.],.],.],.]]],.] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => 100000
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 100000
[[.,[[.,.],[.,[[.,.],.]]]],.] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => 100000
[[.,[[.,.],[[.,.],[.,.]]]],.] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => 100000
[[.,[[.,.],[[.,[.,.]],.]]],.] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => 100000
[[.,[[.,.],[[[.,.],.],.]]],.] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => 100000
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => 100000
[[.,[[.,[.,.]],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => 100000
[[.,[[[.,.],.],[.,[.,.]]]],.] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => 100000
[[.,[[[.,.],.],[[.,.],.]]],.] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => 100000
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 100000
[[.,[[.,[[.,.],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 100000
[[.,[[[.,.],[.,.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => 100000
[[.,[[[.,[.,.]],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => 100000
[[.,[[[[.,.],.],.],[.,.]]],.] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => 100000
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 100000
[[.,[[.,[.,[[.,.],.]]],.]],.] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 100000
[[.,[[.,[[.,.],[.,.]]],.]],.] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 100000
[[.,[[.,[[.,[.,.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 100000
[[.,[[.,[[[.,.],.],.]],.]],.] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => 100000
[[.,[[[.,.],[.,[.,.]]],.]],.] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => 100000
[[.,[[[.,.],[[.,.],.]],.]],.] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => 100000
[[.,[[[.,[.,.]],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => 100000
[[.,[[[[.,.],.],[.,.]],.]],.] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => 100000
[[.,[[[.,[.,[.,.]]],.],.]],.] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => 100000
[[.,[[[.,[[.,.],.]],.],.]],.] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => 100000
[[.,[[[[.,.],[.,.]],.],.]],.] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => 100000
[[.,[[[[.,[.,.]],.],.],.]],.] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => 100000
[[.,[[[[[.,.],.],.],.],.]],.] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => 100000
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => 100001
[[[.,.],[.,[.,[[.,.],.]]]],.] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => 100001
[[[.,.],[.,[[.,.],[.,.]]]],.] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => 100001
[[[.,.],[.,[[.,[.,.]],.]]],.] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => 100001
[[[.,.],[.,[[[.,.],.],.]]],.] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => 100001
[[[.,.],[[.,.],[.,[.,.]]]],.] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => 100001
[[[.,.],[[.,.],[[.,.],.]]],.] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => 100001
[[[.,.],[[.,[.,.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => 100001
[[[.,.],[[[.,.],.],[.,.]]],.] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => 100001
[[[.,.],[[.,[.,[.,.]]],.]],.] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => 100001
[[[.,.],[[.,[[.,.],.]],.]],.] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => 100001
[[[.,.],[[[.,.],[.,.]],.]],.] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => 100001
[[[.,.],[[[.,[.,.]],.],.]],.] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => 100001
[[[.,.],[[[[.,.],.],.],.]],.] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => 100001
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => 100010
[[[.,[.,.]],[.,[[.,.],.]]],.] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => 100010
[[[.,[.,.]],[[.,.],[.,.]]],.] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => 100010
[[[.,[.,.]],[[.,[.,.]],.]],.] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => 100010
[[[.,[.,.]],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => 100010
[[[[.,.],.],[.,[.,[.,.]]]],.] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => 100011
[[[[.,.],.],[.,[[.,.],.]]],.] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => 100011
[[[[.,.],.],[[.,.],[.,.]]],.] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => 100011
[[[[.,.],.],[[.,[.,.]],.]],.] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => 100011
[[[[.,.],.],[[[.,.],.],.]],.] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => 100011
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 100100
[[[.,[.,[.,.]]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => 100100
[[[.,[[.,.],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => 100100
[[[.,[[.,.],.]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => 100100
[[[[.,.],[.,.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => 100101
[[[[.,.],[.,.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => 100101
[[[[.,[.,.]],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => 100110
[[[[.,[.,.]],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => 100110
[[[[[.,.],.],.],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => 100111
[[[[[.,.],.],.],[[.,.],.]],.] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => 100111
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => 101000
[[[.,[.,[[.,.],.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => 101000
[[[.,[[.,.],[.,.]]],[.,.]],.] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => 101000
[[[.,[[.,[.,.]],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 101000
[[[.,[[[.,.],.],.]],[.,.]],.] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => 101000
[[[[.,.],[.,[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => 101001
[[[[.,.],[[.,.],.]],[.,.]],.] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => 101001
[[[[.,[.,.]],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 101010
[[[[[.,.],.],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => 101011
[[[[.,[.,[.,.]]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => 101100
[[[[.,[[.,.],.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => 101100
[[[[[.,.],[.,.]],.],[.,.]],.] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => 101101
[[[[[.,[.,.]],.],.],[.,.]],.] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => 101110
[[[[[[.,.],.],.],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 101111
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => 110000
[[[.,[.,[.,[[.,.],.]]]],.],.] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => 110000
[[[.,[.,[[.,.],[.,.]]]],.],.] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => 110000
[[[.,[.,[[.,[.,.]],.]]],.],.] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => 110000
[[[.,[.,[[[.,.],.],.]]],.],.] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => 110000
[[[.,[[.,.],[.,[.,.]]]],.],.] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => 110000
[[[.,[[.,.],[[.,.],.]]],.],.] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => 110000
[[[.,[[.,[.,.]],[.,.]]],.],.] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => 110000
[[[.,[[[.,.],.],[.,.]]],.],.] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => 110000
[[[.,[[.,[.,[.,.]]],.]],.],.] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => 110000
[[[.,[[.,[[.,.],.]],.]],.],.] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => 110000
[[[.,[[[.,.],[.,.]],.]],.],.] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => 110000
[[[.,[[[.,[.,.]],.],.]],.],.] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => 110000
[[[.,[[[[.,.],.],.],.]],.],.] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => 110000
[[[[.,.],[.,[.,[.,.]]]],.],.] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => 110001
[[[[.,.],[.,[[.,.],.]]],.],.] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => 110001
[[[[.,.],[[.,.],[.,.]]],.],.] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => 110001
[[[[.,.],[[.,[.,.]],.]],.],.] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => 110001
[[[[.,.],[[[.,.],.],.]],.],.] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => 110001
[[[[.,[.,.]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => 110010
[[[[.,[.,.]],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => 110010
[[[[[.,.],.],[.,[.,.]]],.],.] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => 110011
[[[[[.,.],.],[[.,.],.]],.],.] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => 110011
[[[[.,[.,[.,.]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => 110100
[[[[.,[[.,.],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => 110100
[[[[[.,.],[.,.]],[.,.]],.],.] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => 110101
[[[[[.,[.,.]],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => 110110
[[[[[[.,.],.],.],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => 110111
[[[[.,[.,[.,[.,.]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => 111000
[[[[.,[.,[[.,.],.]]],.],.],.] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => 111000
[[[[.,[[.,.],[.,.]]],.],.],.] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => 111000
[[[[.,[[.,[.,.]],.]],.],.],.] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => 111000
[[[[.,[[[.,.],.],.]],.],.],.] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => 111000
[[[[[.,.],[.,[.,.]]],.],.],.] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => 111001
[[[[[.,.],[[.,.],.]],.],.],.] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => 111001
[[[[[.,[.,.]],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => 111010
[[[[[[.,.],.],[.,.]],.],.],.] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => 111011
[[[[[.,[.,[.,.]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => 111100
[[[[[.,[[.,.],.]],.],.],.],.] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => 111100
[[[[[[.,.],[.,.]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 111101
[[[[[[.,[.,.]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 111110
[[[[[[[.,.],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 0000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => 0000000
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 0000000
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => 0000000
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => 0000000
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => 0000000
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => 0000000
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 0000000
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => 0000000
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => 0000000
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => 0000000
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => 0000000
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => 0000000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 0000000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => 0000000
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 0000000
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => 0000000
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => 0000000
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => 0000000
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => 0000000
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => 0000000
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => 0000000
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => 0000000
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [4,7,8,6,5,3,2,1] => 0000000
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => 0000000
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => 0000000
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [4,6,7,8,5,3,2,1] => 0000000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => 0000000
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => 0000000
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => 0000000
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => 0000000
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => 0000000
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [4,5,7,8,6,3,2,1] => 0000000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => 0000000
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => 0000000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => 0000000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => 0000000
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => 0000000
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => 0000000
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => 0000000
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [5,4,7,6,3,8,2,1] => 0000000
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => 0000000
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => 0000000
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => 0000000
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [5,6,4,3,8,7,2,1] => 0000000
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => 0000000
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => 0000000
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => 0000000
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => 0000000
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [4,5,3,7,8,6,2,1] => 0000000
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [4,5,3,7,6,8,2,1] => 0000000
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [5,4,3,6,8,7,2,1] => 0000000
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [4,5,3,6,8,7,2,1] => 0000000
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => 0000000
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => 0000000
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => 0000000
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [4,3,7,6,5,8,2,1] => 0000000
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 0000000
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [4,3,5,7,8,6,2,1] => 0000000
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => 0000000
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [4,3,5,6,8,7,2,1] => 0000000
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => 0000000
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => 0000000
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => 0000000
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => 0000000
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => 0000000
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => 0000000
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [3,5,6,8,7,4,2,1] => 0000000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => 0000000
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [3,7,6,5,4,8,2,1] => 0000000
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => 0000000
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => 0000000
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => 0000000
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1] => 0000000
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => 0000000
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => 0000000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [3,4,5,6,8,7,2,1] => 0000000
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => 0000000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 0000000
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => 0000000
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 0000000
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => 0000000
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => 0000000
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [4,6,7,5,3,2,8,1] => 0000000
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => 0000000
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => 0000000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 0000000
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 0000000
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => 0000000
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [5,4,3,7,6,2,8,1] => 0000000
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => 0000000
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [4,3,6,7,5,2,8,1] => 0000000
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => 0000000
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [3,5,7,6,4,2,8,1] => 0000000
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => 0000000
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => 0000000
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => 0000000
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [3,4,6,5,7,2,8,1] => 0000000
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => 0000000
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => 0000000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => 0000000
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => 0000000
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [4,6,5,3,2,8,7,1] => 0000000
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [4,5,6,3,2,8,7,1] => 0000000
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => 0000000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => 0000000
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => 0000000
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => 0000000
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => 0000000
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => 0000000
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => 0000000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => 0000000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [4,5,3,2,8,7,6,1] => 0000000
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [4,3,5,2,8,7,6,1] => 0000000
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => 0000000
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1] => 0000000
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 0000000
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => 0000000
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => 0000000
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [3,5,4,2,6,7,8,1] => 0000000
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 0000000
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => 0000000
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => 0000000
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [4,3,2,7,8,6,5,1] => 0000000
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [3,4,2,7,8,6,5,1] => 0000000
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [4,3,2,6,8,7,5,1] => 0000000
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => 0000000
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [3,4,2,7,6,5,8,1] => 0000000
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => 0000000
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [4,3,2,6,5,8,7,1] => 0000000
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [3,4,2,6,5,8,7,1] => 0000000
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [4,3,2,6,5,7,8,1] => 0000000
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => 0000000
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1] => 0000000
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [4,3,2,5,6,8,7,1] => 0000000
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [3,4,2,5,6,8,7,1] => 0000000
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 0000000
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 0000000
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => 0000000
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [3,2,6,8,7,5,4,1] => 0000000
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => 0000000
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [3,2,5,6,7,8,4,1] => 0000000
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [3,2,7,6,5,4,8,1] => 0000000
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [3,2,6,7,5,4,8,1] => 0000000
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 0000000
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 0000000
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [3,2,5,4,6,7,8,1] => 0000000
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => 0000000
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1] => 0000000
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => 0000000
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 0000000
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => 0000000
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => 0000000
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [2,7,6,8,5,4,3,1] => 0000000
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => 0000000
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [2,6,7,8,5,4,3,1] => 0000000
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [2,5,8,7,6,4,3,1] => 0000000
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => 0000000
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => 0000000
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [2,5,6,4,8,7,3,1] => 0000000
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [2,6,5,4,7,8,3,1] => 0000000
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [2,5,4,8,7,6,3,1] => 0000000
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => 0000000
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [2,4,7,8,6,5,3,1] => 0000000
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => 0000000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [2,4,6,7,8,5,3,1] => 0000000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [2,4,7,6,5,8,3,1] => 0000000
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [2,4,6,7,5,8,3,1] => 0000000
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => 0000000
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [2,4,6,5,7,8,3,1] => 0000000
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [2,4,5,7,8,6,3,1] => 0000000
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [2,4,5,6,8,7,3,1] => 0000000
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => 0000000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => 0000000
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [2,6,5,7,4,3,8,1] => 0000000
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => 0000000
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => 0000000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => 0000000
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => 0000000
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [2,6,5,4,3,8,7,1] => 0000000
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [2,4,6,5,3,8,7,1] => 0000000
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [2,4,5,6,3,8,7,1] => 0000000
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [2,6,5,4,3,7,8,1] => 0000000
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [2,5,6,4,3,7,8,1] => 0000000
[.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [2,4,6,5,3,7,8,1] => 0000000
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => [2,4,5,6,3,7,8,1] => 0000000
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => 0000000
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [2,4,5,3,8,7,6,1] => 0000000
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => 0000000
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => 0000000
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => 0000000
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => 0000000
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [2,4,5,3,6,8,7,1] => 0000000
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => 0000000
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => 0000000
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => 0000000
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => 0000000
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [2,4,3,6,7,8,5,1] => 0000000
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [2,4,3,7,6,5,8,1] => 0000000
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [2,4,3,6,7,5,8,1] => 0000000
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => 0000000
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => 0000000
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1] => 0000000
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => 0000000
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => 0000000
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => 0000000
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => 0000000
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [2,3,5,8,7,6,4,1] => 0000000
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 0000000
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => 0000000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => 0000000
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [2,3,5,7,6,4,8,1] => 0000000
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => 0000000
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => 0000000
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => [2,3,5,6,4,7,8,1] => 0000000
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [2,3,5,4,8,7,6,1] => 0000000
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => 0000000
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => 0000000
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => 0000000
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [2,3,4,6,8,7,5,1] => 0000000
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => 0000000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => 0000000
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => 0000000
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [2,3,4,6,5,8,7,1] => 0000000
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => 0000000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => 0000000
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => 0000000
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => 0000000
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => 0000000
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 0000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 0000001
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 0000001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 0000001
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 0000001
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 0000001
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 0000001
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => 0000001
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => 0000001
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => 0000001
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => 0000001
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => 0000001
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [4,6,5,7,3,2,1,8] => 0000001
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => 0000001
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => 0000001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => 0000001
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => 0000001
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => 0000001
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [4,5,3,7,6,2,1,8] => 0000001
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => 0000001
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [4,3,7,6,5,2,1,8] => 0000001
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [4,3,6,5,7,2,1,8] => 0000001
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [4,3,5,7,6,2,1,8] => 0000001
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [3,5,7,6,4,2,1,8] => 0000001
[[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [3,5,6,7,4,2,1,8] => 0000001
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [3,6,5,4,7,2,1,8] => 0000001
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [3,5,4,7,6,2,1,8] => 0000001
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => 0000001
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => 0000001
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => 0000001
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => 0000001
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => 0000001
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => 0000001
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => 0000001
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => 0000001
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => 0000001
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => 0000001
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 0000001
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => 0000001
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [4,3,5,2,7,6,1,8] => 0000001
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => 0000001
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [3,4,5,2,7,6,1,8] => 0000001
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => 0000001
[[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [3,5,4,2,6,7,1,8] => 0000001
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [4,3,2,6,5,7,1,8] => 0000001
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [3,4,2,6,5,7,1,8] => 0000001
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => 0000001
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => 0000001
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => 0000001
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => 0000001
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [3,2,6,5,7,4,1,8] => 0000001
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [3,2,5,7,6,4,1,8] => 0000001
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [3,2,5,6,7,4,1,8] => 0000001
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [3,2,6,5,4,7,1,8] => 0000001
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 0000001
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [3,2,4,6,7,5,1,8] => 0000001
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => 0000001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => 0000001
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => 0000001
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => 0000001
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [2,5,6,7,4,3,1,8] => 0000001
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => 0000001
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => 0000001
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => 0000001
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => 0000001
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => 0000001
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => 0000001
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [2,3,6,7,5,4,1,8] => 0000001
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [2,3,6,5,7,4,1,8] => 0000001
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [2,3,5,7,6,4,1,8] => 0000001
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [2,3,5,6,7,4,1,8] => 0000001
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => 0000001
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => 0000001
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => 0000001
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 0000001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => 0000010
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => 0000010
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => 0000010
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => 0000010
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => 0000010
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => 0000010
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => 0000010
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => 0000010
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => 0000010
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [4,5,3,2,6,1,8,7] => 0000010
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [3,5,4,2,6,1,8,7] => 0000010
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [4,3,2,6,5,1,8,7] => 0000010
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => 0000010
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => 0000010
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [2,6,5,4,3,1,8,7] => 0000010
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [2,4,3,5,6,1,8,7] => 0000010
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => 0000010
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 0000011
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => 0000011
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => 0000011
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => 0000011
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => 0000011
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [4,3,6,5,2,1,7,8] => 0000011
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => 0000011
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => 0000011
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => 0000011
[[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => 0000011
[[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [3,5,4,2,6,1,7,8] => 0000011
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => 0000011
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => 0000011
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => 0000011
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => 0000011
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => 0000011
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [2,4,6,5,3,1,7,8] => 0000011
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [[[.,[[.,.],[[[.,.],.],.]]],.],.] => [2,4,5,6,3,1,7,8] => 0000011
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => 0000011
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => 0000011
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => 0000011
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 0000011
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [4,3,5,2,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [3,5,4,2,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [3,2,4,5,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [2,5,4,3,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => 0000100
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => 0000100
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => 0000100
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [3,5,4,2,1,7,8,6] => 0000100
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => 0000100
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => 0000100
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => 0000100
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => 0000101
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [3,5,4,2,1,7,6,8] => 0000101
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [3,4,5,2,1,7,6,8] => 0000101
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => 0000101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => 0000101
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [2,4,5,3,1,7,6,8] => 0000101
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => 0000101
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => 0000101
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => 0000101
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => 0000110
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [4,5,3,2,1,6,8,7] => 0000110
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [4,3,5,2,1,6,8,7] => 0000110
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [3,5,4,2,1,6,8,7] => 0000110
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [3,4,5,2,1,6,8,7] => 0000110
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [3,2,5,4,1,6,8,7] => 0000110
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [2,5,4,3,1,6,8,7] => 0000110
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [2,4,5,3,1,6,8,7] => 0000110
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => 0000110
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [2,3,5,4,1,6,8,7] => 0000110
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => 0000110
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 0000111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => 0000111
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => 0000111
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => 0000111
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => 0000111
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => 0000111
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => 0000111
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => 0000111
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => 0000111
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => 0000111
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => 0000111
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => 0000111
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => 0000111
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 0000111
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 0001000
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => 0001000
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => 0001000
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => 0001000
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => 0001000
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => 0001000
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 0001000
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => 0001000
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => 0001000
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 0001000
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => 0001000
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => 0001000
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => 0001000
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => 0001000
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => 0001000
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => 0001000
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => 0001001
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => 0001001
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => 0001001
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => 0001001
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => 0001010
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => 0001010
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => 0001010
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => 0001010
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => 0001011
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => 0001011
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => 0001011
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => 0001011
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => 0001100
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => 0001100
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [2,4,3,1,5,8,7,6] => 0001100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => 0001100
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => 0001101
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => 0001110
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => 0001110
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 0001111
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => 0001111
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => 0001111
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => 0001111
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => 0001111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 0010000
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => 0010000
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => 0010000
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => 0010000
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => 0010000
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => 0010000
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [2,3,1,6,8,7,5,4] => 0010000
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => 0010000
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [2,3,1,6,7,8,5,4] => 0010000
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => 0010000
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => 0010000
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => 0010000
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => 0010000
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => 0010000
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => 0010000
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => 0010000
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => 0010000
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => 0010000
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => 0010000
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => 0010000
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => 0010001
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [3,2,1,6,5,7,4,8] => 0010001
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [2,3,1,6,5,7,4,8] => 0010001
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [3,2,1,5,7,6,4,8] => 0010001
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => 0010001
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => 0010010
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => 0010010
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => 0010011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [2,3,1,6,5,4,7,8] => 0010011
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [3,2,1,5,6,4,7,8] => 0010011
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [[[[.,[[.,.],.]],[[.,.],.]],.],.] => [2,3,1,5,6,4,7,8] => 0010011
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => 0010101
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => 0010101
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => 0010111
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => 0010111
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => 0011000
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => 0011000
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => 0011000
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [2,3,1,4,7,8,6,5] => 0011000
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => 0011000
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => 0011000
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => 0011001
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [2,3,1,4,6,5,8,7] => 0011010
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 0011100
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [3,2,1,4,5,7,8,6] => 0011100
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => 0011100
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [3,2,1,4,5,7,6,8] => 0011101
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => 0011101
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => 0011110
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => 0011110
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 0011111
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => 0011111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 0100000
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => 0100000
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => 0100000
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => 0100000
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => 0100000
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => 0100000
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => 0100000
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [2,1,6,7,5,4,8,3] => 0100000
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [2,1,5,7,6,4,8,3] => 0100000
[[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [2,1,5,6,7,4,8,3] => 0100000
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => 0100000
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => 0100000
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => 0100000
[[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [2,1,5,4,6,7,8,3] => 0100000
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => 0100000
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [2,1,4,7,8,6,5,3] => 0100000
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => 0100000
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => 0100000
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => 0100000
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => 0100000
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => 0100000
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => 0100000
[[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [2,1,4,5,6,8,7,3] => 0100000
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => 0100000
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8] => 0100001
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => 0100001
[[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [2,1,5,6,7,4,3,8] => 0100001
[[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [2,1,5,4,6,7,3,8] => 0100001
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [2,1,4,5,6,7,3,8] => 0100001
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 0100010
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => 0100010
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 0100010
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => 0100010
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [2,1,5,6,4,3,7,8] => 0100011
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [2,1,4,6,5,3,7,8] => 0100011
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => 0100100
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [2,1,4,5,3,8,7,6] => 0100100
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => 0100101
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => 0100110
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => 0100111
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => 0100111
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => 0101000
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => 0101000
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => 0101000
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [2,1,4,3,6,7,5,8] => 0101001
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => 0101010
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => 0101011
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => 0101100
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => 0101100
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => 0101110
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => 0101111
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => 0110000
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => 0110000
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => 0110000
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => 0110000
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => 0110000
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [2,1,3,6,7,5,4,8] => 0110001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [2,1,3,6,5,4,8,7] => 0110010
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => 0110010
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => 0110100
[[[[.,[[.,.],.]],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [2,1,3,5,4,7,8,6] => 0110100
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => 0110110
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8] => 0110111
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => 0111000
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => 0111000
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => 0111000
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => 0111010
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => 0111011
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => 0111100
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => 0111100
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => 0111101
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => 0111110
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 0111111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 1000000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 1000000
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => 1000000
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => 1000000
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 1000000
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => 1000000
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => 1000000
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => 1000000
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => 1000000
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => 1000000
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => 1000000
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => 1000000
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => 1000000
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => 1000000
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => 1000000
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => 1000000
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => 1000000
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => 1000000
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => 1000000
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => 1000000
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,4,6,5,8,7,3,2] => 1000000
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,4,5,8,7,6,3,2] => 1000000
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => 1000000
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => 1000000
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => 1000000
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => 1000000
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => 1000000
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => 1000000
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,4,6,5,3,8,7,2] => 1000000
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,4,5,6,3,8,7,2] => 1000000
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,5,4,3,6,8,7,2] => 1000000
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => 1000000
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => 1000000
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => 1000000
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => 1000000
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => 1000000
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => 1000000
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,4,3,6,8,7,5,2] => 1000000
[[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,4,3,6,7,8,5,2] => 1000000
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => 1000000
[[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => 1000000
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,4,3,5,8,7,6,2] => 1000000
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => 1000000
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => 1000000
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => 1000000
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,3,7,8,6,5,4,2] => 1000000
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,3,6,8,7,5,4,2] => 1000000
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => 1000000
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => 1000000
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => 1000000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => 1000000
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => 1000000
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => 1000000
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => 1000000
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,3,6,5,4,8,7,2] => 1000000
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => 1000000
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => 1000000
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,3,4,7,6,8,5,2] => 1000000
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,3,4,6,7,8,5,2] => 1000000
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => 1000000
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => 1000000
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => 1000000
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => 1000000
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => 1000000
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => 1000000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => 1000001
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => 1000001
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,6,5,7,4,3,2,8] => 1000001
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,5,6,7,4,3,2,8] => 1000001
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,5,6,4,7,3,2,8] => 1000001
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,4,6,5,7,3,2,8] => 1000001
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,5,4,6,3,7,2,8] => 1000001
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => 1000001
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => 1000001
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => 1000001
[[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,3,6,7,5,4,2,8] => 1000001
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => 1000001
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,3,5,6,7,4,2,8] => 1000001
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => 1000001
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => 1000001
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => 1000001
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => 1000001
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => 1000001
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => 1000010
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => 1000010
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,5,4,6,3,2,8,7] => 1000010
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,3,6,5,4,2,8,7] => 1000010
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => 1000010
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => 1000011
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,5,6,4,3,2,7,8] => 1000011
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => 1000011
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => 1000011
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,4,5,6,3,2,7,8] => 1000011
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => 1000011
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => 1000011
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => 1000011
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => 1000011
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => 1000011
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => 1000011
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => 1000100
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => 1000100
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,5,4,3,2,7,8,6] => 1000100
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => 1000100
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => 1000100
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => 1000101
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => 1000101
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => 1000101
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => 1000110
[[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,3,5,4,2,6,8,7] => 1000110
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => 1000111
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => 1001000
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => 1001000
[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,3,4,2,7,8,6,5] => 1001000
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => 1001000
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,4,3,2,6,8,7,5] => 1001000
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => 1001000
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => 1001000
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 1001001
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,4,3,2,6,7,5,8] => 1001001
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => 1001001
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => 1001010
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => 1001100
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,4,3,2,5,7,8,6] => 1001100
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => 1001100
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => 1001101
[[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,4,3,2,5,6,8,7] => 1001110
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => 1001110
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => 1001111
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => 1001111
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => 1010000
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => 1010000
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => 1010000
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => 1010000
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => 1010000
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,3,2,5,8,7,6,4] => 1010000
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => 1010000
[[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => 1010000
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => 1010001
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => 1010001
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => 1010010
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,3,2,5,6,4,8,7] => 1010010
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => 1010011
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => 1010100
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => 1010100
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => 1010101
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => 1010111
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => 1011000
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => 1011000
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => 1011000
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => 1011001
[[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,3,2,4,6,5,8,7] => 1011010
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => 1011011
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => 1011100
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => 1011100
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => 1011101
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => 1011110
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => 1011111
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => 1100000
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => 1100000
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 1100000
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => 1100000
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => 1100000
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,2,5,6,8,7,4,3] => 1100000
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => 1100000
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => 1100000
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,2,6,5,4,8,7,3] => 1100000
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => 1100000
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => 1100000
[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,2,5,4,7,8,6,3] => 1100000
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,2,5,4,7,6,8,3] => 1100000
[[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,2,5,4,6,8,7,3] => 1100000
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => 1100000
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => 1100000
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,2,4,7,8,6,5,3] => 1100000
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => 1100000
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => 1100000
[[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => 1100000
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,2,4,6,5,8,7,3] => 1100000
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => 1100000
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,2,4,5,7,8,6,3] => 1100000
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => 1100000
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => 1100000
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => 1100001
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,2,6,7,5,4,3,8] => 1100001
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,2,5,7,6,4,3,8] => 1100001
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => 1100001
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => 1100001
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,2,5,4,6,7,3,8] => 1100001
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,2,4,6,7,5,3,8] => 1100001
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => 1100001
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => 1100010
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => 1100011
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => 1100011
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => 1100011
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => 1100100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => 1100100
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => 1100100
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => 1100100
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => 1100101
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => 1100110
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => 1100111
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => 1101000
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,2,4,3,7,8,6,5] => 1101000
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => 1101000
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => 1101000
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => 1101001
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => 1101010
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => 1101011
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => 1101100
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => 1101100
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => 1101101
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => 1101110
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => 1101111
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => 1110000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => 1110000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => 1110000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => 1110000
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => 1110000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => 1110000
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => 1110000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => 1110000
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => 1110000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => 1110000
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => 1110000
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => 1110000
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => 1110000
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => 1110000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => 1110001
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => 1110001
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => 1110001
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => 1110001
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => 1110001
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => 1110010
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => 1110010
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => 1110011
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => 1110011
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => 1110100
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => 1110100
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => 1110101
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => 1110110
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => 1110111
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => 1111000
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => 1111000
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => 1111000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => 1111000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => 1111000
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => 1111001
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => 1111001
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => 1111010
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => 1111011
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => 1111100
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => 1111100
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => 1111101
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => 1111110
[[[[[[[[.,.],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 1111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 00000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => 00000000
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => 00000000
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => 00000000
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => 00000000
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => 00000000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => 00000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 00000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 11111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 000000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => 000000000
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => 00000000
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => 000000000
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => 000000000
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => 000000000
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => 000000000
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => 000000000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => 00000000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => 000000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 00000001
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 000000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 111111111
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [7,9,8,6,5,4,3,2,1] => 00000000
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [4,9,8,7,6,5,3,2,1] => 00000000
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [3,9,8,7,6,5,4,2,1] => 00000000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => 00000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => 10000000
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [6,8,7,9,5,4,3,2,1] => 00000000
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [5,8,7,6,9,4,3,2,1] => 00000000
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [6,10,9,8,7,5,4,3,2,1] => 000000000
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [4,8,7,6,5,9,3,2,1] => 00000000
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [3,8,7,6,5,4,9,2,1] => 00000000
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [2,8,7,6,5,4,3,9,1] => 00000000
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9] => 10000001
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => 100000000
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,3,5,7,9,10,8,6,4,2] => 100000000
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,10,1] => 000000000
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,10,9,2] => 100000000
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => 010101010
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => [[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,10,9,12,11,2] => 10000000000
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => 01010101010
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 01111111
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 011111111
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,9,8] => 01111110
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,9,8,1] => 00000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 0111111111
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [2,1,3,4,5,6,7,8,10,9] => 011111110
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [2,1,3,4,5,6,8,7,9] => 01111101
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [2,1,3,4,5,6,8,9,7] => 01111100
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [2,3,4,5,6,8,9,7,1] => 00000000
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [2,3,4,5,6,7,8,10,9,1] => 000000000
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 0000000000
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => 00111111
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 00000011
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 00111111
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => 001111111
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [2,4,3,1,5,6,7,8,9] => 00011111
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 000000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 00000001
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 00000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 000000001
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => 1000000000
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 00000001
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 000000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 0000000001
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,10,9,1] => 000000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [7,6,5,4,3,2,1,9,8] => 00000010
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [6,5,4,3,2,1,9,8,7] => 00000100
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [5,4,3,2,1,9,8,7,6] => 00001000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [4,3,2,1,9,8,7,6,5] => 00010000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [3,2,1,9,8,7,6,5,4] => 00100000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [2,1,9,8,7,6,5,4,3] => 01000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 00000011
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => 000000010
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [6,5,4,3,2,1,8,9,7] => 00000100
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [7,6,5,4,3,2,1,10,9,8] => 000000100
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => 000001000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [5,4,3,2,1,10,9,8,7,6] => 000010000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => 000100000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [3,2,1,10,9,8,7,6,5,4] => 001000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => 010000000
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => 11000000
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => 11100000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => 11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => 11111000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => 11111100
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => 11111110
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => 110000000
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => 111000000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => 111100000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => 111110000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => 111111000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => 111111100
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9] => 11111101
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => 111111110
[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => 00000000
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => 00000000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => 00000000
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => 00000000
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => 00000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => 000000000
[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => 000000000
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => 000000000
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => 000000000
[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => 000000000
[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => 000000000
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => 000000000
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 00000000
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => 1111111110
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,3,2,4,5,6,7,9,8] => 10111110
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [2,3,1,4,5,6,7,9,8] => 00111110
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [2,4,3,5,6,7,8,9,1] => 00000000
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 00000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 000000000
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,7,6,9,8] => 11111010
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,4,6,5,9,8,7] => 11110100
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,3,5,4,9,8,7,6] => 11101000
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,2,4,3,9,8,7,6,5] => 11010000
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,3,2,9,8,7,6,5,4] => 10100000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => 10000000
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => 11111100
[[[[[[.,[[[.,.],.],.]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => 11111000
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,6,7,8,9,5] => 11110000
[[[[.,[[[[[.,.],.],.],.],.]],.],.],.] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,5,6,7,8,9,4] => 11100000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,3] => 11000000
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => 111111100
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,5,8,7,9,6] => 11111000
[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,6,8,9,10,7] => 111111000
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,4,7,6,8,9,5] => 11110000
[[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,5,7,8,9,10,6] => 111110000
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [1,2,3,6,5,7,8,9,4] => 11100000
[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,4,6,7,8,9,10,5] => 111100000
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [1,2,5,4,6,7,8,9,3] => 11000000
[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,3,5,6,7,8,9,10,4] => 111000000
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,4,3,5,6,7,8,9,2] => 10000000
[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,10,3] => 110000000
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,10,2] => 100000000
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,7,6,8,9] => 11111011
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,6,5,7,8,9] => 11110111
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,2,3,5,4,6,7,8,9] => 11101111
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9] => 11011111
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9] => 10111111
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,9,8,10] => 111111101
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,2,3,4,5,6,8,7,9,10] => 111111011
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,2,3,4,5,7,6,8,9,10] => 111110111
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,2,3,4,6,5,7,8,9,10] => 111101111
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,2,3,5,4,6,7,8,9,10] => 111011111
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,2,4,3,5,6,7,8,9,10] => 110111111
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,3,2,4,5,6,7,8,9,10] => 101111111
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => 00000001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [2,1,8,7,6,5,4,3,9] => 01000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [2,3,1,9,8,7,6,5,4] => 00100000
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => 1111111111
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 000000011
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [6,5,4,3,2,1,8,7,9] => 00000101
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,7,6,5,4,3,2,9,8] => 10000010
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10] => 100000001
[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => 00000001
[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => 000000001
[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.] => [6,7,5,8,4,3,2,1,9] => 00000001
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [2,3,4,5,6,7,1,9,8] => 00000010
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,3,4,5,6,7,8,2,9] => 10000001
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 001111111
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 00011111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 00000111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [2,1,4,3,5,6,7,8,9] => 01011111
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 000111111
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [3,2,1,5,4,6,7,8,9] => 00101111
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 000011111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 000001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 000000111
[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => 00000011
[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [7,6,5,8,4,3,2,1,9] => 00000001
[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => 00000001
[[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.] => [6,5,8,7,4,3,2,1,9] => 00000001
[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [7,6,5,4,3,2,9,8,1] => 00000000
[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [8,7,6,5,4,3,2,9,1,10] => 000000001
[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [5,4,3,2,1,8,7,6,9] => 00001001
[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [7,6,5,4,3,2,1,9,8,10] => 000000101
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => 00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => 0000000000
[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,7,8,10,9,11] => 1111111101
[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,5,6,8,7,10,9] => 111111010
[[[[[[[.,.],.],.],.],.],[[.,.],.]],.] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,3,4,2,5,6,7,8,9] => 10011111
[[[[[[.,.],.],.],.],[[[.,.],.],.]],.] => [[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,3,4,5,2,6,7,8,9] => 10001111
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,4,3,2,5,6,7,8,9] => 10011111
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [7,6,5,4,3,2,8,9,1] => 00000000
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [2,8,7,6,5,4,3,1,9] => 00000001
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [2,1,4,5,6,7,8,9,3] => 01000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10,11] => 0011111111
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,1] => 00000000
[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]] => [.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [5,4,3,2,6,7,8,9,1] => 00000000
[[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [5,6,4,3,2,1,7,8,9,10] => 000001111
[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => [2,1,3,5,6,7,8,9,4] => 01100000
[[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.] => [6,5,7,8,4,3,2,1,9] => 00000001
[[.,.],[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.] => [6,5,4,7,8,3,2,1,9] => 00000001
[[.,.],[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [6,5,4,3,2,7,8,1,9] => 00000001
[[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => [7,6,8,9,5,4,3,2,1,10] => 000000001
[[.,.],[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]] => [[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.] => [7,6,5,8,9,4,3,2,1,10] => 000000001
[[.,.],[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]] => [[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.] => [7,6,5,4,3,8,9,2,1,10] => 000000001
[[.,.],[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.] => [7,6,5,4,3,2,8,9,1,10] => 000000001
[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [8,7,6,5,4,3,2,10,9,1] => 000000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1] => 0000000000
[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]] => [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => 00011111
[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]] => [[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9,10] => 000111111
[[[[[[.,.],.],.],.],[[.,.],.]],[.,.]] => [[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [2,1,4,5,3,6,7,8,9] => 01001111
[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]] => [[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => 00001111
[[[[[[.,.],.],.],.],[.,.]],[[.,.],.]] => [[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [2,3,1,5,4,6,7,8,9] => 00101111
[[[[[[[.,.],.],.],.],[.,.]],[.,.]],.] => [[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [1,3,2,5,4,6,7,8,9] => 10101111
[[[[[[[.,.],.],.],.],[[.,.],.]],.],.] => [[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,2,4,5,3,6,7,8,9] => 11001111
[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => 00000000
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
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.