Identifier
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
[.,.] => [1] => [] =>
[.,[.,.]] => [2,1] => [1] =>
[[.,.],.] => [1,2] => [1] =>
[.,[.,[.,.]]] => [3,2,1] => [2,1] => 1
[.,[[.,.],.]] => [2,3,1] => [2,1] => 1
[[.,.],[.,.]] => [3,1,2] => [1,2] => 0
[[.,[.,.]],.] => [2,1,3] => [2,1] => 1
[[[.,.],.],.] => [1,2,3] => [1,2] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [3,2,1] => 11
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,2,1] => 11
[.,[[.,.],[.,.]]] => [4,2,3,1] => [2,3,1] => 01
[.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,1] => 11
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,1] => 01
[[.,.],[.,[.,.]]] => [4,3,1,2] => [3,1,2] => 01
[[.,.],[[.,.],.]] => [3,4,1,2] => [3,1,2] => 01
[[.,[.,.]],[.,.]] => [4,2,1,3] => [2,1,3] => 10
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,2,3] => 00
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1] => 11
[[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1] => 01
[[[.,.],[.,.]],.] => [3,1,2,4] => [3,1,2] => 01
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3] => 10
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3] => 00
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [4,3,2,1] => 111
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,3,2,1] => 111
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [3,4,2,1] => 101
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [4,3,2,1] => 111
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,4,2,1] => 101
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [4,2,3,1] => 011
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [4,2,3,1] => 011
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [3,2,4,1] => 011
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [2,3,4,1] => 001
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [4,3,2,1] => 111
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [3,4,2,1] => 101
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [4,2,3,1] => 011
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [3,2,4,1] => 011
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [2,3,4,1] => 001
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [4,3,1,2] => 011
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [4,3,1,2] => 011
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [3,4,1,2] => 001
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [4,3,1,2] => 011
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [3,4,1,2] => 001
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [4,2,1,3] => 101
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [4,2,1,3] => 101
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [4,1,2,3] => 001
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [4,1,2,3] => 001
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [3,2,1,4] => 110
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [2,3,1,4] => 010
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [3,1,2,4] => 010
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [2,1,3,4] => 100
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,2,3,4] => 000
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1] => 111
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [3,4,2,1] => 101
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [4,2,3,1] => 011
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [3,2,4,1] => 011
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [2,3,4,1] => 001
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [4,3,1,2] => 011
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [3,4,1,2] => 001
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [4,2,1,3] => 101
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [4,1,2,3] => 001
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4] => 110
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [2,3,1,4] => 010
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [3,1,2,4] => 010
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4] => 100
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4] => 000
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [5,4,3,2,1] => 1111
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,4,3,2,1] => 1111
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [4,5,3,2,1] => 1101
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [5,4,3,2,1] => 1111
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [4,5,3,2,1] => 1101
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [5,3,4,2,1] => 1011
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [5,3,4,2,1] => 1011
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [4,3,5,2,1] => 1011
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [3,4,5,2,1] => 1001
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [5,4,3,2,1] => 1111
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [4,5,3,2,1] => 1101
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [5,3,4,2,1] => 1011
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [4,3,5,2,1] => 1011
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [3,4,5,2,1] => 1001
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [5,4,2,3,1] => 0111
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [5,4,2,3,1] => 0111
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [4,5,2,3,1] => 0101
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [5,4,2,3,1] => 0111
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [4,5,2,3,1] => 0101
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [5,3,2,4,1] => 0111
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [5,3,2,4,1] => 0111
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [5,2,3,4,1] => 0011
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [5,2,3,4,1] => 0011
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [4,3,2,5,1] => 0111
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [3,4,2,5,1] => 0011
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [4,2,3,5,1] => 0011
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [3,2,4,5,1] => 0101
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [2,3,4,5,1] => 0001
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [5,4,3,2,1] => 1111
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [4,5,3,2,1] => 1101
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [5,3,4,2,1] => 1011
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [4,3,5,2,1] => 1011
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [3,4,5,2,1] => 1001
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [5,4,2,3,1] => 0111
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [4,5,2,3,1] => 0101
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [5,3,2,4,1] => 0111
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [5,2,3,4,1] => 0011
>>> Load all 1045 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [4,3,2,5,1] => 0111
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [3,4,2,5,1] => 0011
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [4,2,3,5,1] => 0011
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [3,2,4,5,1] => 0101
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [2,3,4,5,1] => 0001
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [5,4,3,1,2] => 0111
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [5,4,3,1,2] => 0111
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [4,5,3,1,2] => 0101
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [5,4,3,1,2] => 0111
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [4,5,3,1,2] => 0101
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [5,3,4,1,2] => 0011
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [5,3,4,1,2] => 0011
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [4,3,5,1,2] => 0011
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [3,4,5,1,2] => 0001
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [5,4,3,1,2] => 0111
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [4,5,3,1,2] => 0101
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [5,3,4,1,2] => 0011
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [4,3,5,1,2] => 0011
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [3,4,5,1,2] => 0001
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [5,4,2,1,3] => 1011
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [5,4,2,1,3] => 1011
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [4,5,2,1,3] => 1001
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [5,4,2,1,3] => 1011
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [4,5,2,1,3] => 1001
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [5,4,1,2,3] => 0011
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [5,4,1,2,3] => 0011
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [4,5,1,2,3] => 0001
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [5,4,1,2,3] => 0011
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [4,5,1,2,3] => 0001
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [5,3,2,1,4] => 1101
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [5,3,2,1,4] => 1101
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [5,2,3,1,4] => 0101
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [5,2,3,1,4] => 0101
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [5,3,1,2,4] => 0101
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [5,3,1,2,4] => 0101
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [5,2,1,3,4] => 1001
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [5,2,1,3,4] => 1001
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [5,1,2,3,4] => 0001
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [5,1,2,3,4] => 0001
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [4,3,2,1,5] => 1110
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [3,4,2,1,5] => 1010
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [4,2,3,1,5] => 0110
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [3,2,4,1,5] => 0110
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [2,3,4,1,5] => 0010
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [4,3,1,2,5] => 0110
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [3,4,1,2,5] => 0010
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [4,2,1,3,5] => 1010
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [4,1,2,3,5] => 0010
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [3,2,1,4,5] => 1100
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [2,3,1,4,5] => 0100
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [3,1,2,4,5] => 0100
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [2,1,3,4,5] => 1000
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,2,3,4,5] => 0000
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1] => 1111
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [4,5,3,2,1] => 1101
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [5,3,4,2,1] => 1011
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [4,3,5,2,1] => 1011
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [3,4,5,2,1] => 1001
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [5,4,2,3,1] => 0111
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [4,5,2,3,1] => 0101
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [5,3,2,4,1] => 0111
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [5,2,3,4,1] => 0011
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [4,3,2,5,1] => 0111
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [3,4,2,5,1] => 0011
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [4,2,3,5,1] => 0011
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [3,2,4,5,1] => 0101
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [2,3,4,5,1] => 0001
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [5,4,3,1,2] => 0111
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [4,5,3,1,2] => 0101
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [5,3,4,1,2] => 0011
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [4,3,5,1,2] => 0011
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [3,4,5,1,2] => 0001
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [5,4,2,1,3] => 1011
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [4,5,2,1,3] => 1001
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [5,4,1,2,3] => 0011
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [4,5,1,2,3] => 0001
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [5,3,2,1,4] => 1101
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [5,2,3,1,4] => 0101
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [5,3,1,2,4] => 0101
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [5,2,1,3,4] => 1001
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [5,1,2,3,4] => 0001
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5] => 1110
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [3,4,2,1,5] => 1010
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [4,2,3,1,5] => 0110
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [3,2,4,1,5] => 0110
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [2,3,4,1,5] => 0010
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [4,3,1,2,5] => 0110
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [3,4,1,2,5] => 0010
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [4,2,1,3,5] => 1010
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [4,1,2,3,5] => 0010
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5] => 1100
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [2,3,1,4,5] => 0100
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [3,1,2,4,5] => 0100
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5] => 1000
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5] => 0000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [5,6,4,3,2,1] => 11101
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [5,6,4,3,2,1] => 11101
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [6,4,5,3,2,1] => 11011
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [6,4,5,3,2,1] => 11011
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [5,4,6,3,2,1] => 11011
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [4,5,6,3,2,1] => 11001
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [6,5,4,3,2,1] => 11111
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [5,6,4,3,2,1] => 11101
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [6,4,5,3,2,1] => 11011
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [5,4,6,3,2,1] => 11011
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,5,6,3,2,1] => 11001
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [6,5,3,4,2,1] => 10111
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [6,5,3,4,2,1] => 10111
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [5,6,3,4,2,1] => 10101
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [6,5,3,4,2,1] => 10111
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [5,6,3,4,2,1] => 10101
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [6,4,3,5,2,1] => 10111
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [6,4,3,5,2,1] => 10111
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [6,3,4,5,2,1] => 10011
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [6,3,4,5,2,1] => 10011
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [5,4,3,6,2,1] => 10111
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [4,5,3,6,2,1] => 10011
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [5,3,4,6,2,1] => 10011
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [4,3,5,6,2,1] => 10101
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [3,4,5,6,2,1] => 10001
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [6,5,4,3,2,1] => 11111
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [5,6,4,3,2,1] => 11101
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [6,4,5,3,2,1] => 11011
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [5,4,6,3,2,1] => 11011
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [4,5,6,3,2,1] => 11001
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [6,5,3,4,2,1] => 10111
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [5,6,3,4,2,1] => 10101
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [6,4,3,5,2,1] => 10111
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [6,3,4,5,2,1] => 10011
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [5,4,3,6,2,1] => 10111
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [4,5,3,6,2,1] => 10011
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [5,3,4,6,2,1] => 10011
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [4,3,5,6,2,1] => 10101
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [3,4,5,6,2,1] => 10001
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [6,5,4,2,3,1] => 01111
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [6,5,4,2,3,1] => 01111
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [5,6,4,2,3,1] => 01101
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [6,5,4,2,3,1] => 01111
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [5,6,4,2,3,1] => 01101
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [6,4,5,2,3,1] => 01011
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [6,4,5,2,3,1] => 01011
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [5,4,6,2,3,1] => 01011
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [4,5,6,2,3,1] => 01001
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [6,5,4,2,3,1] => 01111
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [5,6,4,2,3,1] => 01101
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [6,4,5,2,3,1] => 01011
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [5,4,6,2,3,1] => 01011
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [4,5,6,2,3,1] => 01001
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [6,5,3,2,4,1] => 01111
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [6,5,3,2,4,1] => 01111
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [5,6,3,2,4,1] => 01101
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [6,5,3,2,4,1] => 01111
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [5,6,3,2,4,1] => 01101
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [6,5,2,3,4,1] => 00111
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [6,5,2,3,4,1] => 00111
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [5,6,2,3,4,1] => 00101
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [6,5,2,3,4,1] => 00111
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [5,6,2,3,4,1] => 00101
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [6,4,3,2,5,1] => 01111
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [6,4,3,2,5,1] => 01111
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [6,3,4,2,5,1] => 00111
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [6,3,4,2,5,1] => 00111
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [6,4,2,3,5,1] => 00111
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [6,4,2,3,5,1] => 00111
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [6,3,2,4,5,1] => 01011
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [6,3,2,4,5,1] => 01011
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [6,2,3,4,5,1] => 00011
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [6,2,3,4,5,1] => 00011
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1] => 01111
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [4,5,3,2,6,1] => 01011
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [5,3,4,2,6,1] => 00111
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [4,3,5,2,6,1] => 00111
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [3,4,5,2,6,1] => 00011
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [5,4,2,3,6,1] => 00111
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [4,5,2,3,6,1] => 00011
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [5,3,2,4,6,1] => 01011
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [5,2,3,4,6,1] => 00011
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [4,3,2,5,6,1] => 01101
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [3,4,2,5,6,1] => 00101
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [4,2,3,5,6,1] => 00101
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [3,2,4,5,6,1] => 01001
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1] => 00001
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [6,5,4,3,2,1] => 11111
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [5,6,4,3,2,1] => 11101
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [6,4,5,3,2,1] => 11011
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [5,4,6,3,2,1] => 11011
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [4,5,6,3,2,1] => 11001
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [6,5,3,4,2,1] => 10111
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [5,6,3,4,2,1] => 10101
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [6,4,3,5,2,1] => 10111
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [6,3,4,5,2,1] => 10011
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [5,4,3,6,2,1] => 10111
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [4,5,3,6,2,1] => 10011
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [5,3,4,6,2,1] => 10011
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [4,3,5,6,2,1] => 10101
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [3,4,5,6,2,1] => 10001
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [6,5,4,2,3,1] => 01111
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [5,6,4,2,3,1] => 01101
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [6,4,5,2,3,1] => 01011
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [5,4,6,2,3,1] => 01011
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [4,5,6,2,3,1] => 01001
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [6,5,3,2,4,1] => 01111
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [5,6,3,2,4,1] => 01101
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [6,5,2,3,4,1] => 00111
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [5,6,2,3,4,1] => 00101
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [6,4,3,2,5,1] => 01111
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [6,3,4,2,5,1] => 00111
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [6,4,2,3,5,1] => 00111
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [6,3,2,4,5,1] => 01011
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [6,2,3,4,5,1] => 00011
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [5,4,3,2,6,1] => 01111
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [4,5,3,2,6,1] => 01011
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [5,3,4,2,6,1] => 00111
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [4,3,5,2,6,1] => 00111
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [3,4,5,2,6,1] => 00011
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [5,4,2,3,6,1] => 00111
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [4,5,2,3,6,1] => 00011
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [5,3,2,4,6,1] => 01011
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [5,2,3,4,6,1] => 00011
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [4,3,2,5,6,1] => 01101
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [3,4,2,5,6,1] => 00101
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [4,2,3,5,6,1] => 00101
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [3,2,4,5,6,1] => 01001
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,3,4,5,6,1] => 00001
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [6,5,4,3,1,2] => 01111
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [6,5,4,3,1,2] => 01111
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [5,6,4,3,1,2] => 01101
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [6,5,4,3,1,2] => 01111
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [5,6,4,3,1,2] => 01101
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [6,4,5,3,1,2] => 01011
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [6,4,5,3,1,2] => 01011
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [5,4,6,3,1,2] => 01011
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [4,5,6,3,1,2] => 01001
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [6,5,4,3,1,2] => 01111
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [5,6,4,3,1,2] => 01101
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [6,4,5,3,1,2] => 01011
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [5,4,6,3,1,2] => 01011
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [4,5,6,3,1,2] => 01001
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [6,5,3,4,1,2] => 00111
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [6,5,3,4,1,2] => 00111
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [5,6,3,4,1,2] => 00101
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [6,5,3,4,1,2] => 00111
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [5,6,3,4,1,2] => 00101
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [6,4,3,5,1,2] => 00111
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [6,4,3,5,1,2] => 00111
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [6,3,4,5,1,2] => 00011
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [6,3,4,5,1,2] => 00011
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [5,4,3,6,1,2] => 00111
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [4,5,3,6,1,2] => 00011
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [5,3,4,6,1,2] => 00011
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [4,3,5,6,1,2] => 00101
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [3,4,5,6,1,2] => 00001
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [6,5,4,3,1,2] => 01111
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [5,6,4,3,1,2] => 01101
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [6,4,5,3,1,2] => 01011
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [5,4,6,3,1,2] => 01011
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [4,5,6,3,1,2] => 01001
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [6,5,3,4,1,2] => 00111
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [5,6,3,4,1,2] => 00101
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [6,4,3,5,1,2] => 00111
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [6,3,4,5,1,2] => 00011
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [5,4,3,6,1,2] => 00111
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [4,5,3,6,1,2] => 00011
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [5,3,4,6,1,2] => 00011
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [4,3,5,6,1,2] => 00101
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [3,4,5,6,1,2] => 00001
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [6,5,4,2,1,3] => 10111
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [6,5,4,2,1,3] => 10111
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [5,6,4,2,1,3] => 10101
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [6,5,4,2,1,3] => 10111
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [5,6,4,2,1,3] => 10101
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [6,4,5,2,1,3] => 10011
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [6,4,5,2,1,3] => 10011
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [5,4,6,2,1,3] => 10011
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [4,5,6,2,1,3] => 10001
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [6,5,4,2,1,3] => 10111
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [5,6,4,2,1,3] => 10101
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [6,4,5,2,1,3] => 10011
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [5,4,6,2,1,3] => 10011
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [4,5,6,2,1,3] => 10001
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [6,5,4,1,2,3] => 00111
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [6,5,4,1,2,3] => 00111
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [5,6,4,1,2,3] => 00101
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [6,5,4,1,2,3] => 00111
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [5,6,4,1,2,3] => 00101
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [6,4,5,1,2,3] => 00011
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [6,4,5,1,2,3] => 00011
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [5,4,6,1,2,3] => 00011
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [4,5,6,1,2,3] => 00001
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [6,5,4,1,2,3] => 00111
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [5,6,4,1,2,3] => 00101
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [6,4,5,1,2,3] => 00011
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [5,4,6,1,2,3] => 00011
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [4,5,6,1,2,3] => 00001
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [6,5,3,2,1,4] => 11011
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [6,5,3,2,1,4] => 11011
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [5,6,3,2,1,4] => 11001
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [6,5,3,2,1,4] => 11011
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [5,6,3,2,1,4] => 11001
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [6,5,2,3,1,4] => 01011
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [6,5,2,3,1,4] => 01011
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [5,6,2,3,1,4] => 01001
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [6,5,2,3,1,4] => 01011
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [5,6,2,3,1,4] => 01001
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [6,5,3,1,2,4] => 01011
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [6,5,3,1,2,4] => 01011
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [5,6,3,1,2,4] => 01001
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [6,5,3,1,2,4] => 01011
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [5,6,3,1,2,4] => 01001
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [6,5,2,1,3,4] => 10011
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [6,5,2,1,3,4] => 10011
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [5,6,2,1,3,4] => 10001
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [6,5,2,1,3,4] => 10011
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [5,6,2,1,3,4] => 10001
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [6,5,1,2,3,4] => 00011
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [6,5,1,2,3,4] => 00011
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [5,6,1,2,3,4] => 00001
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [6,5,1,2,3,4] => 00011
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [5,6,1,2,3,4] => 00001
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [6,4,3,2,1,5] => 11101
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [6,4,3,2,1,5] => 11101
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [6,3,4,2,1,5] => 10101
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [6,3,4,2,1,5] => 10101
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [6,4,2,3,1,5] => 01101
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [6,4,2,3,1,5] => 01101
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [6,3,2,4,1,5] => 01101
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [6,3,2,4,1,5] => 01101
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [6,2,3,4,1,5] => 00101
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [6,2,3,4,1,5] => 00101
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [6,4,3,1,2,5] => 01101
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [6,4,3,1,2,5] => 01101
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [6,3,4,1,2,5] => 00101
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [6,3,4,1,2,5] => 00101
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [6,4,2,1,3,5] => 10101
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [6,4,2,1,3,5] => 10101
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [6,4,1,2,3,5] => 00101
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [6,4,1,2,3,5] => 00101
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [6,3,2,1,4,5] => 11001
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [6,3,2,1,4,5] => 11001
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [6,2,3,1,4,5] => 01001
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [6,2,3,1,4,5] => 01001
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [6,3,1,2,4,5] => 01001
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [6,3,1,2,4,5] => 01001
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [6,2,1,3,4,5] => 10001
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [6,2,1,3,4,5] => 10001
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [6,1,2,3,4,5] => 00001
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [6,1,2,3,4,5] => 00001
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [5,4,3,2,1,6] => 11110
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [4,5,3,2,1,6] => 11010
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [5,3,4,2,1,6] => 10110
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [4,3,5,2,1,6] => 10110
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [3,4,5,2,1,6] => 10010
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [5,4,2,3,1,6] => 01110
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [4,5,2,3,1,6] => 01010
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [5,3,2,4,1,6] => 01110
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [5,2,3,4,1,6] => 00110
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [4,3,2,5,1,6] => 01110
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [3,4,2,5,1,6] => 00110
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [4,2,3,5,1,6] => 00110
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [3,2,4,5,1,6] => 01010
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [2,3,4,5,1,6] => 00010
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [5,4,3,1,2,6] => 01110
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [4,5,3,1,2,6] => 01010
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [5,3,4,1,2,6] => 00110
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [4,3,5,1,2,6] => 00110
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [3,4,5,1,2,6] => 00010
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [5,4,2,1,3,6] => 10110
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [4,5,2,1,3,6] => 10010
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [5,4,1,2,3,6] => 00110
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [4,5,1,2,3,6] => 00010
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [5,3,2,1,4,6] => 11010
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [5,2,3,1,4,6] => 01010
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [5,3,1,2,4,6] => 01010
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [5,2,1,3,4,6] => 10010
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [5,1,2,3,4,6] => 00010
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [4,3,2,1,5,6] => 11100
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [3,4,2,1,5,6] => 10100
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [4,2,3,1,5,6] => 01100
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [3,2,4,1,5,6] => 01100
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [2,3,4,1,5,6] => 00100
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [4,3,1,2,5,6] => 01100
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [3,4,1,2,5,6] => 00100
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [4,2,1,3,5,6] => 10100
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [4,1,2,3,5,6] => 00100
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [3,2,1,4,5,6] => 11000
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [2,3,1,4,5,6] => 01000
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [3,1,2,4,5,6] => 01000
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [2,1,3,4,5,6] => 10000
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6] => 00000
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1] => 11111
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1] => 11101
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [6,4,5,3,2,1] => 11011
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1] => 11011
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1] => 11001
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [6,5,3,4,2,1] => 10111
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [5,6,3,4,2,1] => 10101
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [6,4,3,5,2,1] => 10111
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [6,3,4,5,2,1] => 10011
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1] => 10111
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1] => 10011
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [5,3,4,6,2,1] => 10011
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1] => 10101
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1] => 10001
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [6,5,4,2,3,1] => 01111
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [5,6,4,2,3,1] => 01101
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [6,4,5,2,3,1] => 01011
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [5,4,6,2,3,1] => 01011
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [4,5,6,2,3,1] => 01001
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [6,5,3,2,4,1] => 01111
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [5,6,3,2,4,1] => 01101
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [6,5,2,3,4,1] => 00111
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [5,6,2,3,4,1] => 00101
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [6,4,3,2,5,1] => 01111
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [6,3,4,2,5,1] => 00111
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [6,4,2,3,5,1] => 00111
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [6,3,2,4,5,1] => 01011
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [6,2,3,4,5,1] => 00011
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1] => 01111
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1] => 01011
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [5,3,4,2,6,1] => 00111
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1] => 00111
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1] => 00011
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [5,4,2,3,6,1] => 00111
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [4,5,2,3,6,1] => 00011
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [5,3,2,4,6,1] => 01011
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [5,2,3,4,6,1] => 00011
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1] => 01101
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1] => 00101
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [4,2,3,5,6,1] => 00101
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1] => 01001
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1] => 00001
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [6,5,4,3,1,2] => 01111
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [5,6,4,3,1,2] => 01101
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [6,4,5,3,1,2] => 01011
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [5,4,6,3,1,2] => 01011
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [4,5,6,3,1,2] => 01001
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [6,5,3,4,1,2] => 00111
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [5,6,3,4,1,2] => 00101
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [6,4,3,5,1,2] => 00111
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [6,3,4,5,1,2] => 00011
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [5,4,3,6,1,2] => 00111
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [4,5,3,6,1,2] => 00011
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [5,3,4,6,1,2] => 00011
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [4,3,5,6,1,2] => 00101
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [3,4,5,6,1,2] => 00001
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [6,5,4,2,1,3] => 10111
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [5,6,4,2,1,3] => 10101
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [6,4,5,2,1,3] => 10011
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [5,4,6,2,1,3] => 10011
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [4,5,6,2,1,3] => 10001
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [6,5,4,1,2,3] => 00111
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [5,6,4,1,2,3] => 00101
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [6,4,5,1,2,3] => 00011
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [5,4,6,1,2,3] => 00011
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [4,5,6,1,2,3] => 00001
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [6,5,3,2,1,4] => 11011
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [5,6,3,2,1,4] => 11001
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [6,5,2,3,1,4] => 01011
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [5,6,2,3,1,4] => 01001
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [6,5,3,1,2,4] => 01011
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [5,6,3,1,2,4] => 01001
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [6,5,2,1,3,4] => 10011
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [5,6,2,1,3,4] => 10001
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [6,5,1,2,3,4] => 00011
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [5,6,1,2,3,4] => 00001
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [6,4,3,2,1,5] => 11101
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [6,3,4,2,1,5] => 10101
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [6,4,2,3,1,5] => 01101
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [6,3,2,4,1,5] => 01101
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [6,2,3,4,1,5] => 00101
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [6,4,3,1,2,5] => 01101
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [6,3,4,1,2,5] => 00101
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [6,4,2,1,3,5] => 10101
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [6,4,1,2,3,5] => 00101
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [6,3,2,1,4,5] => 11001
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [6,2,3,1,4,5] => 01001
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [6,3,1,2,4,5] => 01001
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [6,2,1,3,4,5] => 10001
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5] => 00001
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6] => 11110
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6] => 11010
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [5,3,4,2,1,6] => 10110
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6] => 10110
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6] => 10010
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [5,4,2,3,1,6] => 01110
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [4,5,2,3,1,6] => 01010
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [5,3,2,4,1,6] => 01110
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [5,2,3,4,1,6] => 00110
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6] => 01110
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6] => 00110
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [4,2,3,5,1,6] => 00110
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6] => 01010
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6] => 00010
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [5,4,3,1,2,6] => 01110
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [4,5,3,1,2,6] => 01010
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [5,3,4,1,2,6] => 00110
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [4,3,5,1,2,6] => 00110
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [3,4,5,1,2,6] => 00010
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [5,4,2,1,3,6] => 10110
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [4,5,2,1,3,6] => 10010
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [5,4,1,2,3,6] => 00110
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [4,5,1,2,3,6] => 00010
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [5,3,2,1,4,6] => 11010
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [5,2,3,1,4,6] => 01010
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [5,3,1,2,4,6] => 01010
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [5,2,1,3,4,6] => 10010
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6] => 00010
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6] => 11100
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6] => 10100
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [4,2,3,1,5,6] => 01100
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6] => 01100
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6] => 00100
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [4,3,1,2,5,6] => 01100
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [3,4,1,2,5,6] => 00100
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [4,2,1,3,5,6] => 10100
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6] => 00100
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6] => 11000
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6] => 01000
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6] => 01000
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6] => 10000
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6] => 00000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [6,7,5,4,3,2,1] => 111101
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [7,5,6,4,3,2,1] => 111011
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [7,5,6,4,3,2,1] => 111011
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [6,5,7,4,3,2,1] => 111011
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [5,6,7,4,3,2,1] => 111001
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1] => 110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [7,6,4,5,3,2,1] => 110111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [6,7,4,5,3,2,1] => 110101
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [6,5,7,4,3,2,1] => 111011
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [7,6,4,5,3,2,1] => 110111
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => [7,5,4,6,3,2,1] => 110111
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [7,4,5,6,3,2,1] => 110011
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [4,5,6,7,3,2,1] => 110001
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [7,6,5,3,4,2,1] => 101111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [7,6,5,3,4,2,1] => 101111
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [6,7,5,3,4,2,1] => 101101
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [7,5,6,3,4,2,1] => 101011
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => [5,6,7,3,4,2,1] => 101001
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => [6,7,3,4,5,2,1] => 100101
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => [7,5,4,3,6,2,1] => 101111
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [6,4,5,7,3,8,2,1] => [6,4,5,7,3,2,1] => 110011
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,2,1] => 110101
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [7,6,5,3,4,2,1] => 101111
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => [7,6,4,3,5,2,1] => 101111
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [7,6,3,4,5,2,1] => 100111
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => [6,3,4,5,7,2,1] => 100011
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,2,1] => 101001
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [7,6,5,4,2,3,1] => 011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [7,6,5,4,2,3,1] => 011111
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [6,7,5,4,2,3,1] => 011101
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [7,5,6,4,2,3,1] => 011011
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [5,6,7,4,2,3,1] => 011001
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [7,6,4,5,2,3,1] => 010111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [6,7,4,5,2,3,1] => 010101
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => [4,5,6,7,2,3,1] => 010001
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => [7,6,5,3,2,4,1] => 011111
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => [6,5,7,3,2,4,1] => 011011
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => [5,6,7,3,2,4,1] => 011001
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [7,6,5,2,3,4,1] => 001111
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => [6,7,5,2,3,4,1] => 001101
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => [5,6,7,2,3,4,1] => 001001
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => [5,6,7,2,3,4,1] => 001001
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => [7,3,2,4,5,6,1] => 010011
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,1] => 111111
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,1] => 111101
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,1] => 111011
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => [6,4,5,7,3,2,1] => 110011
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,1] => 101111
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,1] => 100111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => [6,5,3,4,7,2,1] => 100111
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [7,6,5,4,2,3,1] => 011111
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => [6,7,4,5,2,3,1] => 010101
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => [6,4,5,7,2,3,1] => 010011
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => [4,5,6,7,2,3,1] => 010001
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => [7,6,5,3,2,4,1] => 011111
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [7,6,5,2,3,4,1] => 001111
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => [6,7,2,3,4,5,1] => 000101
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,1] => 011101
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,1] => 000101
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => [5,2,3,4,6,7,1] => 000101
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,1] => 011001
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,1] => 001001
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => [4,2,3,5,6,7,1] => 001001
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,1] => 010001
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,1] => 000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => 011111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => 011111
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [6,7,5,4,3,1,2] => 011101
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [7,5,6,4,3,1,2] => 011011
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [6,5,7,4,3,1,2] => 011011
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [5,6,7,4,3,1,2] => 011001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [7,6,4,5,3,1,2] => 010111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [7,6,4,5,3,1,2] => 010111
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [4,5,6,7,3,1,2] => 010001
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [7,6,5,3,4,1,2] => 001111
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [7,5,6,3,4,1,2] => 001011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [7,5,6,3,4,1,2] => 001011
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [7,6,5,3,4,1,2] => 001111
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => [6,7,5,3,4,1,2] => 001101
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [7,5,6,3,4,1,2] => 001011
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [6,5,7,3,4,1,2] => 001011
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [5,6,7,3,4,1,2] => 001001
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [7,5,4,3,6,1,2] => 001111
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => [7,4,5,3,6,1,2] => 000111
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [7,5,3,4,6,1,2] => 000111
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [7,4,3,5,6,1,2] => 001011
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [7,3,4,5,6,1,2] => 000011
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [4,3,5,6,7,1,2] => 001001
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [3,4,5,6,7,1,2] => 000001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [7,6,5,4,3,1,2] => 011111
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => [6,5,7,4,3,1,2] => 011011
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => [5,6,7,4,3,1,2] => 011001
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [6,7,4,5,3,1,2] => 010101
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => [5,6,4,7,3,1,2] => 010011
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => [5,4,6,7,3,1,2] => 010101
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => [5,4,6,3,7,1,2] => 000111
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => [5,6,3,4,7,1,2] => 000011
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => [6,4,3,5,7,1,2] => 001011
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [6,3,4,5,7,1,2] => 000011
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => [5,4,3,6,7,1,2] => 001101
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => [4,5,3,6,7,1,2] => 000101
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => [4,3,5,6,7,1,2] => 001001
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [3,4,5,6,7,1,2] => 000001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => [7,6,5,4,2,1,3] => 101111
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => [7,6,5,4,2,1,3] => 101111
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => [5,6,7,4,2,1,3] => 101001
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => [4,5,6,7,2,1,3] => 100001
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [7,6,5,4,1,2,3] => 001111
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [6,7,5,4,1,2,3] => 001101
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [5,6,7,4,1,2,3] => 001001
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [6,5,7,4,1,2,3] => 001011
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [5,6,7,4,1,2,3] => 001001
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [7,6,4,5,1,2,3] => 000111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [6,7,4,5,1,2,3] => 000101
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [7,4,5,6,1,2,3] => 000011
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [7,4,5,6,1,2,3] => 000011
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => [6,7,4,5,1,2,3] => 000101
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => [6,5,4,7,1,2,3] => 000111
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [4,5,6,7,1,2,3] => 000001
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => [7,6,5,3,2,1,4] => 110111
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => [7,5,6,3,2,1,4] => 110011
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => [7,6,5,3,2,1,4] => 110111
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => [5,6,7,3,2,1,4] => 110001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => [7,6,5,2,3,1,4] => 010111
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [7,8,5,6,2,3,1,4] => [7,5,6,2,3,1,4] => 010011
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => [6,7,5,2,3,1,4] => 010101
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => [7,5,6,2,3,1,4] => 010011
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => [5,6,7,2,3,1,4] => 010001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [7,6,5,3,1,2,4] => 010111
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [7,5,6,3,1,2,4] => 010011
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => [6,7,5,3,1,2,4] => 010101
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => [7,5,6,3,1,2,4] => 010011
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => [5,6,7,3,1,2,4] => 010001
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [7,6,5,2,1,3,4] => 100111
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [7,6,5,2,1,3,4] => 100111
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [6,7,5,2,1,3,4] => 100101
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [7,5,6,2,1,3,4] => 100011
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => [6,5,7,2,1,3,4] => 100011
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => [5,6,7,2,1,3,4] => 100001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => 000111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => 000111
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [6,7,5,1,2,3,4] => 000101
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [7,6,5,1,2,3,4] => 000111
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [6,7,5,1,2,3,4] => 000101
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [7,5,6,1,2,3,4] => 000011
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [7,5,6,1,2,3,4] => 000011
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [6,5,7,1,2,3,4] => 000011
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [5,6,7,1,2,3,4] => 000001
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [7,6,5,1,2,3,4] => 000111
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => [6,7,5,1,2,3,4] => 000101
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [7,5,6,1,2,3,4] => 000011
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => [6,5,7,1,2,3,4] => 000011
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [5,6,7,1,2,3,4] => 000001
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => [7,6,4,3,2,1,5] => 111011
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => [6,7,4,3,2,1,5] => 111001
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => [7,6,3,4,2,1,5] => 101011
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => [6,7,3,4,2,1,5] => 101001
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => [7,6,4,2,3,1,5] => 011011
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => [6,7,4,2,3,1,5] => 011001
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => [7,6,3,2,4,1,5] => 011011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => [6,7,3,2,4,1,5] => 011001
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => [7,6,2,3,4,1,5] => 001011
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => [6,7,2,3,4,1,5] => 001001
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [7,6,4,3,1,2,5] => 011011
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [6,7,4,3,1,2,5] => 011001
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [7,6,3,4,1,2,5] => 001011
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => [6,7,3,4,1,2,5] => 001001
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => [7,6,4,2,1,3,5] => 101011
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => [6,7,4,2,1,3,5] => 101001
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [7,6,4,1,2,3,5] => 001011
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [6,7,4,1,2,3,5] => 001001
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => [7,6,3,2,1,4,5] => 110011
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => [6,7,3,2,1,4,5] => 110001
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => [7,6,2,3,1,4,5] => 010011
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => [6,7,2,3,1,4,5] => 010001
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => [7,6,3,1,2,4,5] => 010011
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => [6,7,3,1,2,4,5] => 010001
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [7,6,2,1,3,4,5] => 100011
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => [6,7,2,1,3,4,5] => 100001
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [7,6,1,2,3,4,5] => 000011
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [7,6,1,2,3,4,5] => 000011
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [6,7,1,2,3,4,5] => 000001
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [7,6,1,2,3,4,5] => 000011
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [6,7,1,2,3,4,5] => 000001
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => [7,5,4,3,2,1,6] => 111101
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [7,8,4,5,2,3,1,6] => [7,4,5,2,3,1,6] => 010101
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => [7,3,4,2,5,1,6] => 001101
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => [7,5,4,2,1,3,6] => 101101
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [7,5,4,1,2,3,6] => 001101
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [7,4,5,1,2,3,6] => 000101
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => [7,5,2,1,3,4,6] => 100101
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => [7,5,2,1,3,4,6] => 100101
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [7,5,1,2,3,4,6] => 000101
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [7,5,1,2,3,4,6] => 000101
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6] => [7,4,3,2,1,5,6] => 111001
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => [7,4,3,2,1,5,6] => 111001
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => [7,3,2,4,1,5,6] => 011001
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => [7,2,3,4,1,5,6] => 001001
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [7,3,4,1,2,5,6] => 001001
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => [7,4,2,1,3,5,6] => 101001
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [7,4,1,2,3,5,6] => 001001
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => [7,3,2,1,4,5,6] => 110001
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => [7,3,2,1,4,5,6] => 110001
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [7,2,1,3,4,5,6] => 100001
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => 000001
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => 000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 111110
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => 110010
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [6,5,4,3,1,2,7] => 011110
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [5,6,3,4,1,2,7] => 001010
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [8,4,3,5,6,1,2,7] => [4,3,5,6,1,2,7] => 001010
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => [3,4,5,6,1,2,7] => 000010
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => [6,5,4,2,1,3,7] => 101110
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [6,4,5,1,2,3,7] => 000110
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => [6,5,2,3,1,4,7] => 010110
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => [5,6,2,3,1,4,7] => 010010
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => [5,6,2,1,3,4,7] => 100010
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [6,5,1,2,3,4,7] => 000110
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [5,6,1,2,3,4,7] => 000010
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => [6,4,3,2,1,5,7] => 111010
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => [6,3,4,2,1,5,7] => 101010
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => [6,4,2,1,3,5,7] => 101010
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 111000
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => 001000
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => 001000
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 110000
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => 010000
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => 010000
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 100000
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1] => 111111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1] => 111101
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1] => 111011
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1] => 111001
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => [7,6,4,5,3,2,1] => 110111
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => [7,4,5,6,3,2,1] => 110011
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1] => 110111
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => [7,5,6,3,4,2,1] => 101011
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => [5,6,7,3,4,2,1] => 101001
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => [7,6,4,3,5,2,1] => 101111
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => [7,6,3,4,5,2,1] => 100111
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => [7,5,4,3,6,2,1] => 101111
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => [6,7,5,4,2,3,1] => 011101
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => [5,6,7,4,2,3,1] => 011001
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => [7,6,4,5,2,3,1] => 010111
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => [6,7,4,5,2,3,1] => 010101
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [7,4,5,6,2,3,1,8] => [7,4,5,6,2,3,1] => 010011
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => [5,6,4,7,2,3,1] => 010011
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => [6,5,7,3,2,4,1] => 011011
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => [5,6,7,3,2,4,1] => 011001
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => [7,6,5,2,3,4,1] => 001111
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => [6,7,5,2,3,4,1] => 001101
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => [7,5,6,2,3,4,1] => 001011
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => [6,5,7,2,3,4,1] => 001011
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => [5,6,7,2,3,4,1] => 001001
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => [6,7,3,4,2,5,1] => 001101
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => [7,4,5,2,3,6,1] => 000111
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => [5,6,3,4,2,7,1] => 001011
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1] => 000111
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1] => 011101
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1] => 010001
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1] => 000001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [7,6,5,4,3,1,2] => 011111
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => [7,5,6,4,3,1,2] => 011011
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [7,4,5,6,3,1,2,8] => [7,4,5,6,3,1,2] => 010011
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => [7,6,5,4,2,1,3] => 101111
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => [6,5,7,4,2,1,3] => 101011
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [7,5,4,6,2,1,3] => 100111
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => [7,4,5,6,2,1,3] => 100011
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [7,6,5,4,1,2,3] => 001111
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [5,6,7,4,1,2,3] => 001001
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [7,4,5,6,1,2,3] => 000011
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => [5,6,4,7,1,2,3] => 000011
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => [5,4,6,7,1,2,3] => 000101
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => [5,6,7,3,1,2,4] => 010001
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => [5,6,7,2,1,3,4] => 100001
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [7,6,5,1,2,3,4] => 000111
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => [6,7,5,1,2,3,4] => 000101
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => [7,5,6,1,2,3,4] => 000011
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => [6,5,7,1,2,3,4] => 000011
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [5,6,7,1,2,3,4] => 000001
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => [7,6,4,3,2,1,5] => 111011
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => [7,6,4,3,1,2,5] => 011011
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [6,7,1,2,3,4,5] => 000001
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => [7,5,3,1,2,4,6] => 010101
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [7,5,1,2,3,4,6] => 000101
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => [7,4,3,2,1,5,6] => 111001
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => [7,3,1,2,4,5,6] => 010001
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [7,2,1,3,4,5,6] => 100001
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6] => 000001
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7] => 111110
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7] => 011110
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7] => 010110
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => [4,2,3,5,6,1,7] => 001010
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7] => 000010
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => [5,6,4,3,1,2,7] => 011010
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => [5,4,6,3,1,2,7] => 010110
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => [5,6,3,4,1,2,7] => 001010
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => [5,4,3,6,1,2,7] => 001110
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => [5,6,4,2,1,3,7] => 101010
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => [5,4,6,2,1,3,7] => 100110
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => [4,5,6,1,2,3,7] => 000010
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => [5,6,3,2,1,4,7] => 110010
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => [6,4,3,2,1,5,7] => 111010
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => [6,4,3,1,2,5,7] => 011010
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => [6,4,1,2,3,5,7] => 001010
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => [6,2,3,1,4,5,7] => 010010
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7] => 000010
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7] => 111100
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => [4,5,2,3,1,6,7] => 010100
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => [5,2,3,4,1,6,7] => 001100
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7] => 000100
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => [5,3,1,2,4,6,7] => 010100
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7] => 000100
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7] => 111000
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7] => 011000
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7] => 001000
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => [3,4,1,2,5,6,7] => 001000
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7] => 001000
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7] => 110000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7] => 010000
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7] => 100000
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7] => 000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [7,8,6,5,4,3,2,1] => 1111101
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,1] => 0000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8] => 0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [6,7,8,9,5,4,3,2,1] => 11110001
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [3,4,5,6,7,8,1,2] => 0000001
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,1] => 00000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9] => 00000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [8,7,6,5,4,3,2,1] => 1111111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,1] => 1111111
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1] => 1111111
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => [8,6,7,5,4,3,2,1] => 1111011
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [8,7,5,6,9,4,3,2,1] => [8,7,5,6,4,3,2,1] => 1110111
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [8,7,6,4,5,9,3,2,1] => [8,7,6,4,5,3,2,1] => 1101111
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [8,7,6,5,3,4,9,2,1] => [8,7,6,5,3,4,2,1] => 1011111
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,2,3,9,1] => [8,7,6,5,4,2,3,1] => 0111111
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => [8,7,6,5,4,3,1,2] => 0111111
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1] => 11111111
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [9,7,8,5,6,3,4,1,2] => 00101011
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 00000000
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1000000
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,1] => 0100001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 000000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 10000000
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => 0100000
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => 0100000
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => [4,2,3,5,6,7,8,1] => 0010001
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [3,4,2,5,6,7,8,1] => 0010001
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [3,2,4,5,6,7,8,9,1] => 01000001
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,1] => 000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => 0000001
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => [7,8,1,2,3,4,5,6] => 0000001
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [6,7,8,1,2,3,4,5] => 0000001
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => 0000001
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => 00000001
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => [8,9,1,2,3,4,5,6,7] => 00000001
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => [7,8,9,1,2,3,4,5,6] => 00000001
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => [6,7,8,9,1,2,3,4,5] => 00000001
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => [3,4,5,6,7,8,9,1,2] => 00000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [8,7,6,5,4,3,1,2] => 0111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [7,8,6,5,4,3,2,1] => 1111101
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [9,8,7,6,5,4,3,1,2] => 01111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [8,9,7,6,5,4,3,2,1] => 11111101
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [7,6,8,5,4,3,2,1] => 1111011
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [8,7,6,5,4,1,2,3] => 0011111
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8] => 1111110
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8] => 1111100
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8] => 1111000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8] => 1110000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8] => 1100000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8] => 1000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9] => 11111110
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9] => 11111100
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9] => 11111000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9] => 11110000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9] => 11100000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9] => 11000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9] => 10000000
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10] => 100000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1] => 0000001
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8] => 0000010
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1] => 00000001
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => [7,1,2,3,4,5,6,8] => 0000010
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7] => 0000001
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8] => 00000001
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [9,8,7,6,5,4,1,2,3] => 00111111
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => 00000001
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [8,7,1,2,3,4,5,6] => 0000011
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [8,7,6,1,2,3,4,5] => 0000111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [8,7,6,5,1,2,3,4] => 0001111
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => [9,8,1,2,3,4,5,6,7] => 00000011
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => [9,8,7,1,2,3,4,5,6] => 00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => [9,8,7,6,1,2,3,4,5] => 00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => [9,8,7,6,5,1,2,3,4] => 00011111
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8] => 0010000
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.