Identifier
Mp00017: Binary trees —to 312-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
[[.,.],[.,.]] => [1,3,2] => [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
[.,[[.,.],[.,.]]] => [2,4,3,1] => [2,3,1] => 01
[.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,1] => 11
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,1] => 01
[[.,.],[.,[.,.]]] => [1,4,3,2] => [1,3,2] => 01
[[.,.],[[.,.],.]] => [1,3,4,2] => [1,3,2] => 01
[[.,[.,.]],[.,.]] => [2,1,4,3] => [2,1,3] => 10
[[[.,.],.],[.,.]] => [1,2,4,3] => [1,2,3] => 00
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1] => 11
[[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1] => 01
[[[.,.],[.,.]],.] => [1,3,2,4] => [1,3,2] => 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
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [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
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [2,4,3,1] => 011
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [2,4,3,1] => 011
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [3,2,4,1] => 011
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [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
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [2,4,3,1] => 011
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [3,2,4,1] => 011
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [2,3,4,1] => 001
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [1,4,3,2] => 011
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [1,4,3,2] => 011
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [1,3,4,2] => 001
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [1,4,3,2] => 011
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [1,3,4,2] => 001
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [2,1,4,3] => 101
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,1,4,3] => 101
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [1,2,4,3] => 001
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [1,2,4,3] => 001
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [3,2,1,4] => 110
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [2,3,1,4] => 010
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [1,3,2,4] => 010
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,1,3,4] => 100
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [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
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [2,4,3,1] => 011
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [3,2,4,1] => 011
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [2,3,4,1] => 001
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [1,4,3,2] => 011
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [1,3,4,2] => 001
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,1,4,3] => 101
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [1,2,4,3] => 001
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4] => 110
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [2,3,1,4] => 010
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [1,3,2,4] => 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
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [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
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [3,5,4,2,1] => 1011
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [3,5,4,2,1] => 1011
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [4,3,5,2,1] => 1011
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [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
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [3,5,4,2,1] => 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
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [2,5,4,3,1] => 0111
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [2,5,4,3,1] => 0111
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [2,4,5,3,1] => 0101
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [2,5,4,3,1] => 0111
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [2,4,5,3,1] => 0101
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [3,2,5,4,1] => 0111
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [3,2,5,4,1] => 0111
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [2,3,5,4,1] => 0011
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [2,3,5,4,1] => 0011
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [4,3,2,5,1] => 0111
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [3,4,2,5,1] => 0011
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [2,4,3,5,1] => 0011
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [3,2,4,5,1] => 0101
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [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
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [3,5,4,2,1] => 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
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [2,5,4,3,1] => 0111
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [2,4,5,3,1] => 0101
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [3,2,5,4,1] => 0111
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [2,3,5,4,1] => 0011
>>> Load all 1043 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
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [2,4,3,5,1] => 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
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [1,5,4,3,2] => 0111
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [1,5,4,3,2] => 0111
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [1,4,5,3,2] => 0101
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [1,5,4,3,2] => 0111
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [1,4,5,3,2] => 0101
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [1,3,5,4,2] => 0011
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [1,3,5,4,2] => 0011
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [1,4,3,5,2] => 0011
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [1,3,4,5,2] => 0001
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [1,5,4,3,2] => 0111
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [1,4,5,3,2] => 0101
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [1,3,5,4,2] => 0011
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [1,4,3,5,2] => 0011
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [1,3,4,5,2] => 0001
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [2,1,5,4,3] => 1011
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [2,1,5,4,3] => 1011
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [2,1,4,5,3] => 1001
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [2,1,5,4,3] => 1011
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,1,4,5,3] => 1001
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [1,2,5,4,3] => 0011
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [1,2,5,4,3] => 0011
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [1,2,4,5,3] => 0001
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [1,2,5,4,3] => 0011
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [1,2,4,5,3] => 0001
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [3,2,1,5,4] => 1101
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [3,2,1,5,4] => 1101
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [2,3,1,5,4] => 0101
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [2,3,1,5,4] => 0101
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [1,3,2,5,4] => 0101
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [1,3,2,5,4] => 0101
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [2,1,3,5,4] => 1001
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,1,3,5,4] => 1001
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [1,2,3,5,4] => 0001
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [1,2,3,5,4] => 0001
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [4,3,2,1,5] => 1110
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [3,4,2,1,5] => 1010
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [2,4,3,1,5] => 0110
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [3,2,4,1,5] => 0110
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [2,3,4,1,5] => 0010
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [1,4,3,2,5] => 0110
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [1,3,4,2,5] => 0010
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,1,4,3,5] => 1010
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [1,2,4,3,5] => 0010
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [3,2,1,4,5] => 1100
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [2,3,1,4,5] => 0100
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [1,3,2,4,5] => 0100
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,1,3,4,5] => 1000
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [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
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [3,5,4,2,1] => 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
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [2,5,4,3,1] => 0111
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [2,4,5,3,1] => 0101
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [3,2,5,4,1] => 0111
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [2,3,5,4,1] => 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
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [2,4,3,5,1] => 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
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [1,5,4,3,2] => 0111
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [1,4,5,3,2] => 0101
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [1,3,5,4,2] => 0011
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [1,4,3,5,2] => 0011
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [1,3,4,5,2] => 0001
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [2,1,5,4,3] => 1011
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,1,4,5,3] => 1001
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [1,2,5,4,3] => 0011
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [1,2,4,5,3] => 0001
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [3,2,1,5,4] => 1101
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [2,3,1,5,4] => 0101
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [1,3,2,5,4] => 0101
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,1,3,5,4] => 1001
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [1,2,3,5,4] => 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
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [2,4,3,1,5] => 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
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [1,4,3,2,5] => 0110
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [1,3,4,2,5] => 0010
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,1,4,3,5] => 1010
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [1,2,4,3,5] => 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
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [1,3,2,4,5] => 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
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [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
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [4,6,5,3,2,1] => 11011
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [4,6,5,3,2,1] => 11011
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [5,4,6,3,2,1] => 11011
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [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
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [4,6,5,3,2,1] => 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
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [3,6,5,4,2,1] => 10111
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [3,6,5,4,2,1] => 10111
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [3,5,6,4,2,1] => 10101
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [3,6,5,4,2,1] => 10111
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [3,5,6,4,2,1] => 10101
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [4,3,6,5,2,1] => 10111
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [4,3,6,5,2,1] => 10111
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [3,4,6,5,2,1] => 10011
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [3,4,6,5,2,1] => 10011
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [5,4,3,6,2,1] => 10111
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [4,5,3,6,2,1] => 10011
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [3,5,4,6,2,1] => 10011
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [4,3,5,6,2,1] => 10101
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [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
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [4,6,5,3,2,1] => 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
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [3,6,5,4,2,1] => 10111
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [3,5,6,4,2,1] => 10101
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [4,3,6,5,2,1] => 10111
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [3,4,6,5,2,1] => 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
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [3,5,4,6,2,1] => 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
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [2,6,5,4,3,1] => 01111
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [2,6,5,4,3,1] => 01111
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [2,5,6,4,3,1] => 01101
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [2,6,5,4,3,1] => 01111
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [2,5,6,4,3,1] => 01101
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [2,4,6,5,3,1] => 01011
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [2,4,6,5,3,1] => 01011
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [2,5,4,6,3,1] => 01011
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [2,4,5,6,3,1] => 01001
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [2,6,5,4,3,1] => 01111
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [2,5,6,4,3,1] => 01101
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [2,4,6,5,3,1] => 01011
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [2,5,4,6,3,1] => 01011
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [2,4,5,6,3,1] => 01001
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [3,2,6,5,4,1] => 01111
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [3,2,6,5,4,1] => 01111
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [3,2,5,6,4,1] => 01101
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [3,2,6,5,4,1] => 01111
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [3,2,5,6,4,1] => 01101
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [2,3,6,5,4,1] => 00111
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [2,3,6,5,4,1] => 00111
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [2,3,5,6,4,1] => 00101
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [2,3,6,5,4,1] => 00111
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [2,3,5,6,4,1] => 00101
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [4,3,2,6,5,1] => 01111
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [4,3,2,6,5,1] => 01111
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [3,4,2,6,5,1] => 00111
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [3,4,2,6,5,1] => 00111
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [2,4,3,6,5,1] => 00111
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [2,4,3,6,5,1] => 00111
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [3,2,4,6,5,1] => 01011
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [3,2,4,6,5,1] => 01011
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [2,3,4,6,5,1] => 00011
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [2,3,4,6,5,1] => 00011
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [5,4,3,2,6,1] => 01111
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [4,5,3,2,6,1] => 01011
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [3,5,4,2,6,1] => 00111
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [4,3,5,2,6,1] => 00111
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [3,4,5,2,6,1] => 00011
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [2,5,4,3,6,1] => 00111
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [2,4,5,3,6,1] => 00011
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [3,2,5,4,6,1] => 01011
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [2,3,5,4,6,1] => 00011
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [4,3,2,5,6,1] => 01101
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [3,4,2,5,6,1] => 00101
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [2,4,3,5,6,1] => 00101
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [3,2,4,5,6,1] => 01001
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [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
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [4,6,5,3,2,1] => 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
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [3,6,5,4,2,1] => 10111
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [3,5,6,4,2,1] => 10101
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [4,3,6,5,2,1] => 10111
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [3,4,6,5,2,1] => 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
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [3,5,4,6,2,1] => 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
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [2,6,5,4,3,1] => 01111
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [2,5,6,4,3,1] => 01101
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [2,4,6,5,3,1] => 01011
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [2,5,4,6,3,1] => 01011
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [2,4,5,6,3,1] => 01001
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [3,2,6,5,4,1] => 01111
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [3,2,5,6,4,1] => 01101
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [2,3,6,5,4,1] => 00111
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [2,3,5,6,4,1] => 00101
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [4,3,2,6,5,1] => 01111
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [3,4,2,6,5,1] => 00111
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [2,4,3,6,5,1] => 00111
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [3,2,4,6,5,1] => 01011
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [2,3,4,6,5,1] => 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
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [3,5,4,2,6,1] => 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
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [2,5,4,3,6,1] => 00111
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [2,4,5,3,6,1] => 00011
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [3,2,5,4,6,1] => 01011
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [2,3,5,4,6,1] => 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
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [2,4,3,5,6,1] => 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
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [1,6,5,4,3,2] => 01111
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [1,6,5,4,3,2] => 01111
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [1,5,6,4,3,2] => 01101
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [1,6,5,4,3,2] => 01111
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [1,5,6,4,3,2] => 01101
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [1,4,6,5,3,2] => 01011
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [1,4,6,5,3,2] => 01011
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [1,5,4,6,3,2] => 01011
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [1,4,5,6,3,2] => 01001
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [1,6,5,4,3,2] => 01111
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [1,5,6,4,3,2] => 01101
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [1,4,6,5,3,2] => 01011
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [1,5,4,6,3,2] => 01011
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [1,4,5,6,3,2] => 01001
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [1,3,6,5,4,2] => 00111
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [1,3,6,5,4,2] => 00111
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [1,3,5,6,4,2] => 00101
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [1,3,6,5,4,2] => 00111
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [1,3,5,6,4,2] => 00101
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [1,4,3,6,5,2] => 00111
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [1,4,3,6,5,2] => 00111
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [1,3,4,6,5,2] => 00011
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [1,3,4,6,5,2] => 00011
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [1,5,4,3,6,2] => 00111
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [1,4,5,3,6,2] => 00011
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [1,3,5,4,6,2] => 00011
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [1,4,3,5,6,2] => 00101
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [1,3,4,5,6,2] => 00001
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [1,6,5,4,3,2] => 01111
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [1,5,6,4,3,2] => 01101
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [1,4,6,5,3,2] => 01011
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [1,5,4,6,3,2] => 01011
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [1,4,5,6,3,2] => 01001
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [1,3,6,5,4,2] => 00111
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [1,3,5,6,4,2] => 00101
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [1,4,3,6,5,2] => 00111
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [1,3,4,6,5,2] => 00011
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [1,5,4,3,6,2] => 00111
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [1,4,5,3,6,2] => 00011
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [1,3,5,4,6,2] => 00011
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [1,4,3,5,6,2] => 00101
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [1,3,4,5,6,2] => 00001
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [2,1,6,5,4,3] => 10111
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [2,1,6,5,4,3] => 10111
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [2,1,5,6,4,3] => 10101
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [2,1,6,5,4,3] => 10111
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [2,1,5,6,4,3] => 10101
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [2,1,4,6,5,3] => 10011
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [2,1,4,6,5,3] => 10011
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [2,1,5,4,6,3] => 10011
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [2,1,4,5,6,3] => 10001
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [2,1,6,5,4,3] => 10111
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [2,1,5,6,4,3] => 10101
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [2,1,4,6,5,3] => 10011
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [2,1,5,4,6,3] => 10011
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [2,1,4,5,6,3] => 10001
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [1,2,6,5,4,3] => 00111
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [1,2,6,5,4,3] => 00111
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [1,2,5,6,4,3] => 00101
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [1,2,6,5,4,3] => 00111
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [1,2,5,6,4,3] => 00101
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [1,2,4,6,5,3] => 00011
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [1,2,4,6,5,3] => 00011
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [1,2,5,4,6,3] => 00011
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [1,2,4,5,6,3] => 00001
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [1,2,6,5,4,3] => 00111
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [1,2,5,6,4,3] => 00101
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [1,2,4,6,5,3] => 00011
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [1,2,5,4,6,3] => 00011
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [1,2,4,5,6,3] => 00001
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [3,2,1,6,5,4] => 11011
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [3,2,1,6,5,4] => 11011
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [3,2,1,5,6,4] => 11001
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [3,2,1,6,5,4] => 11011
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [3,2,1,5,6,4] => 11001
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [2,3,1,6,5,4] => 01011
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [2,3,1,6,5,4] => 01011
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [2,3,1,5,6,4] => 01001
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [2,3,1,6,5,4] => 01011
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [2,3,1,5,6,4] => 01001
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [1,3,2,6,5,4] => 01011
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [1,3,2,6,5,4] => 01011
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [1,3,2,5,6,4] => 01001
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [1,3,2,6,5,4] => 01011
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [1,3,2,5,6,4] => 01001
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [2,1,3,6,5,4] => 10011
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [2,1,3,6,5,4] => 10011
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [2,1,3,5,6,4] => 10001
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [2,1,3,6,5,4] => 10011
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [2,1,3,5,6,4] => 10001
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [1,2,3,6,5,4] => 00011
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [1,2,3,6,5,4] => 00011
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [1,2,3,5,6,4] => 00001
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [1,2,3,6,5,4] => 00011
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [1,2,3,5,6,4] => 00001
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [4,3,2,1,6,5] => 11101
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [4,3,2,1,6,5] => 11101
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [3,4,2,1,6,5] => 10101
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [3,4,2,1,6,5] => 10101
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [2,4,3,1,6,5] => 01101
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [2,4,3,1,6,5] => 01101
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [3,2,4,1,6,5] => 01101
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [3,2,4,1,6,5] => 01101
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [2,3,4,1,6,5] => 00101
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [2,3,4,1,6,5] => 00101
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [1,4,3,2,6,5] => 01101
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [1,4,3,2,6,5] => 01101
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [1,3,4,2,6,5] => 00101
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [1,3,4,2,6,5] => 00101
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [2,1,4,3,6,5] => 10101
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [2,1,4,3,6,5] => 10101
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [1,2,4,3,6,5] => 00101
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [1,2,4,3,6,5] => 00101
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [3,2,1,4,6,5] => 11001
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [3,2,1,4,6,5] => 11001
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [2,3,1,4,6,5] => 01001
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [2,3,1,4,6,5] => 01001
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [1,3,2,4,6,5] => 01001
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [1,3,2,4,6,5] => 01001
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [2,1,3,4,6,5] => 10001
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [2,1,3,4,6,5] => 10001
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [1,2,3,4,6,5] => 00001
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [1,2,3,4,6,5] => 00001
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [5,4,3,2,1,6] => 11110
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [4,5,3,2,1,6] => 11010
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [3,5,4,2,1,6] => 10110
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [4,3,5,2,1,6] => 10110
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [3,4,5,2,1,6] => 10010
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [2,5,4,3,1,6] => 01110
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [2,4,5,3,1,6] => 01010
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [3,2,5,4,1,6] => 01110
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [2,3,5,4,1,6] => 00110
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [4,3,2,5,1,6] => 01110
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [3,4,2,5,1,6] => 00110
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [2,4,3,5,1,6] => 00110
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [3,2,4,5,1,6] => 01010
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [2,3,4,5,1,6] => 00010
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [1,5,4,3,2,6] => 01110
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [1,4,5,3,2,6] => 01010
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [1,3,5,4,2,6] => 00110
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [1,4,3,5,2,6] => 00110
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [1,3,4,5,2,6] => 00010
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [2,1,5,4,3,6] => 10110
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [2,1,4,5,3,6] => 10010
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [1,2,5,4,3,6] => 00110
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [1,2,4,5,3,6] => 00010
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [3,2,1,5,4,6] => 11010
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [2,3,1,5,4,6] => 01010
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [1,3,2,5,4,6] => 01010
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [2,1,3,5,4,6] => 10010
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [1,2,3,5,4,6] => 00010
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [4,3,2,1,5,6] => 11100
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [3,4,2,1,5,6] => 10100
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [2,4,3,1,5,6] => 01100
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [3,2,4,1,5,6] => 01100
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [2,3,4,1,5,6] => 00100
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [1,4,3,2,5,6] => 01100
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [1,3,4,2,5,6] => 00100
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [2,1,4,3,5,6] => 10100
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [1,2,4,3,5,6] => 00100
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [3,2,1,4,5,6] => 11000
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [2,3,1,4,5,6] => 01000
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [1,3,2,4,5,6] => 01000
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [2,1,3,4,5,6] => 10000
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [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
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [4,6,5,3,2,1] => 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
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [3,6,5,4,2,1] => 10111
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [3,5,6,4,2,1] => 10101
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [4,3,6,5,2,1] => 10111
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [3,4,6,5,2,1] => 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
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [3,5,4,6,2,1] => 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
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [2,6,5,4,3,1] => 01111
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [2,5,6,4,3,1] => 01101
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [2,4,6,5,3,1] => 01011
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [2,5,4,6,3,1] => 01011
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [2,4,5,6,3,1] => 01001
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [3,2,6,5,4,1] => 01111
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [3,2,5,6,4,1] => 01101
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [2,3,6,5,4,1] => 00111
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [2,3,5,6,4,1] => 00101
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [4,3,2,6,5,1] => 01111
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [3,4,2,6,5,1] => 00111
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [2,4,3,6,5,1] => 00111
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [3,2,4,6,5,1] => 01011
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [2,3,4,6,5,1] => 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
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [3,5,4,2,6,1] => 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
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [2,5,4,3,6,1] => 00111
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [2,4,5,3,6,1] => 00011
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [3,2,5,4,6,1] => 01011
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [2,3,5,4,6,1] => 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
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [2,4,3,5,6,1] => 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
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2] => 01111
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [1,5,6,4,3,2] => 01101
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [1,4,6,5,3,2] => 01011
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [1,5,4,6,3,2] => 01011
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [1,4,5,6,3,2] => 01001
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [1,3,6,5,4,2] => 00111
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [1,3,5,6,4,2] => 00101
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [1,4,3,6,5,2] => 00111
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [1,3,4,6,5,2] => 00011
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [1,5,4,3,6,2] => 00111
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [1,4,5,3,6,2] => 00011
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [1,3,5,4,6,2] => 00011
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [1,4,3,5,6,2] => 00101
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [1,3,4,5,6,2] => 00001
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3] => 10111
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [2,1,5,6,4,3] => 10101
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [2,1,4,6,5,3] => 10011
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [2,1,5,4,6,3] => 10011
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [2,1,4,5,6,3] => 10001
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3] => 00111
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [1,2,5,6,4,3] => 00101
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [1,2,4,6,5,3] => 00011
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [1,2,5,4,6,3] => 00011
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [1,2,4,5,6,3] => 00001
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4] => 11011
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [3,2,1,5,6,4] => 11001
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [2,3,1,6,5,4] => 01011
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [2,3,1,5,6,4] => 01001
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4] => 01011
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [1,3,2,5,6,4] => 01001
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4] => 10011
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [2,1,3,5,6,4] => 10001
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4] => 00011
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [1,2,3,5,6,4] => 00001
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5] => 11101
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [3,4,2,1,6,5] => 10101
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [2,4,3,1,6,5] => 01101
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [3,2,4,1,6,5] => 01101
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [2,3,4,1,6,5] => 00101
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5] => 01101
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [1,3,4,2,6,5] => 00101
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5] => 10101
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5] => 00101
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5] => 11001
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [2,3,1,4,6,5] => 01001
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5] => 01001
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5] => 10001
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5] => 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
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [3,5,4,2,1,6] => 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
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [2,5,4,3,1,6] => 01110
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [2,4,5,3,1,6] => 01010
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [3,2,5,4,1,6] => 01110
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [2,3,5,4,1,6] => 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
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [2,4,3,5,1,6] => 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
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6] => 01110
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [1,4,5,3,2,6] => 01010
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [1,3,5,4,2,6] => 00110
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [1,4,3,5,2,6] => 00110
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [1,3,4,5,2,6] => 00010
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6] => 10110
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [2,1,4,5,3,6] => 10010
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6] => 00110
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [1,2,4,5,3,6] => 00010
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6] => 11010
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [2,3,1,5,4,6] => 01010
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6] => 01010
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6] => 10010
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6] => 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
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [2,4,3,1,5,6] => 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
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6] => 01100
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [1,3,4,2,5,6] => 00100
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6] => 10100
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6] => 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
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6] => 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
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => [5,7,6,4,3,2,1] => 111011
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => [6,5,7,4,3,2,1] => 111011
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [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
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => [4,7,6,5,3,2,1] => 110111
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [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
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => [4,7,6,5,3,2,1] => 110111
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [4,5,6,7,3,2,1] => 110001
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => [3,7,6,5,4,2,1] => 101111
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => [3,5,7,6,4,2,1] => 101011
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => [3,5,6,7,4,2,1] => 101001
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => [3,4,7,6,5,2,1] => 100111
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => [3,4,5,7,6,2,1] => 100011
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => [4,3,6,5,7,2,1] => 101011
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,2,1] => 111111
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => [5,7,6,4,3,2,1] => 111011
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,2,1] => 110101
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,2,1] => 101001
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => [2,7,6,5,4,3,1] => 011111
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => [2,6,7,5,4,3,1] => 011101
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => [2,5,6,7,4,3,1] => 011001
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => [2,4,7,6,5,3,1] => 010111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => [2,4,6,7,5,3,1] => 010101
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => [2,7,6,5,4,3,1] => 011111
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => [2,3,5,6,7,4,1] => 001001
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => [2,3,5,6,7,4,1] => 001001
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => [4,3,2,7,6,5,1] => 011111
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => [3,4,2,7,6,5,1] => 001111
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => [2,4,3,7,6,5,1] => 001111
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => [3,2,4,7,6,5,1] => 010111
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => [2,3,4,7,6,5,1] => 000111
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => [5,4,3,2,7,6,1] => 011111
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => [5,4,3,2,7,6,1] => 011111
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => [2,5,4,3,7,6,1] => 001111
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => [2,5,4,3,7,6,1] => 001111
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => [2,4,5,3,7,6,1] => 000111
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [3,4,2,5,7,8,6,1] => [3,4,2,5,7,6,1] => 001011
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => [4,3,6,5,2,7,1] => 001111
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => [3,2,6,5,4,7,1] => 010111
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => [2,4,3,6,5,7,1] => 001011
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => [5,4,3,2,6,7,1] => 011101
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => [2,5,4,3,6,7,1] => 001101
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => [2,4,3,5,6,7,1] => 001001
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => [2,3,4,5,6,7,1] => 000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [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
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,1] => 101111
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,1] => 100111
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [4,3,6,5,7,2,1] => 101011
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => [2,5,4,7,6,3,1] => 010111
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => [2,5,4,6,7,3,1] => 010101
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [3,2,6,5,7,4,1] => 011011
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => [4,3,2,7,6,5,1] => 011111
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => [3,4,2,6,7,5,1] => 001101
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1] => [5,4,3,2,7,6,1] => 011111
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [4,3,5,2,7,6,1] => 001111
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => [2,5,4,3,7,6,1] => 001111
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [3,2,5,4,7,6,1] => 010111
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => [2,3,5,4,7,6,1] => 000111
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => [3,2,4,5,7,6,1] => 010011
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => [2,4,3,6,5,7,1] => 001011
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [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
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => [2,5,4,3,6,7,1] => 001101
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [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
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [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
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 011111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [1,7,6,5,4,3,2] => 011111
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => [1,6,7,5,4,3,2] => 011101
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => [1,7,6,5,4,3,2] => 011111
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => [1,6,7,5,4,3,2] => 011101
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => [1,5,7,6,4,3,2] => 011011
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => [1,7,6,5,4,3,2] => 011111
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => [1,5,6,7,4,3,2] => 011001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => [1,4,7,6,5,3,2] => 010111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => [1,4,7,6,5,3,2] => 010111
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => [1,3,5,7,6,4,2] => 001011
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => [1,3,6,5,7,4,2] => 001011
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => [1,3,5,6,7,4,2] => 001001
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => [1,4,3,7,6,5,2] => 001111
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => [1,4,3,7,6,5,2] => 001111
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => [1,3,4,7,6,5,2] => 000111
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => [1,3,4,5,7,6,2] => 000011
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => [1,6,5,4,3,7,2] => 001111
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => [1,5,6,4,3,7,2] => 001011
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => [1,4,3,6,5,7,2] => 001011
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => [1,3,4,5,6,7,2] => 000001
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => [1,5,4,3,6,7,2] => 001101
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => [1,4,5,3,6,7,2] => 000101
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [1,4,3,5,6,7,2] => 001001
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => [1,3,4,5,6,7,2] => 000001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [2,1,7,6,5,4,3] => 101111
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [2,1,6,7,5,4,3] => 101101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => [2,1,6,5,7,4,3] => 101011
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => [2,1,7,6,5,4,3] => 101111
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => [2,1,6,7,5,4,3] => 101101
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => [2,1,6,5,7,4,3] => 101011
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => [2,1,5,6,7,4,3] => 101001
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => [2,1,4,7,6,5,3] => 100111
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => [2,1,4,5,7,6,3] => 100011
[[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => [2,1,4,5,7,6,3] => 100011
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => [2,1,4,6,5,7,3] => 100011
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [2,1,6,5,7,4,3] => 101011
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [2,1,5,4,7,6,3] => 100111
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => [2,1,4,5,6,7,3] => 100001
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => [1,2,6,7,5,4,3] => 001101
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => [1,2,5,6,7,4,3] => 001001
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [1,2,4,7,6,5,3] => 000111
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => [1,2,4,6,7,5,3] => 000101
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => [1,2,6,5,4,7,3] => 000111
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => [1,2,5,6,4,7,3] => 000011
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [1,2,5,4,6,7,3] => 000101
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => [1,2,4,5,6,7,3] => 000001
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => [3,2,1,7,6,5,4] => 110111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => [3,2,1,7,6,5,4] => 110111
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => [3,2,1,6,7,5,4] => 110101
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => [3,2,1,7,6,5,4] => 110111
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => [3,2,1,6,7,5,4] => 110101
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => [3,2,1,5,7,6,4] => 110011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => [3,2,1,5,7,6,4] => 110011
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => [3,2,1,6,5,7,4] => 110011
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => [3,2,1,5,6,7,4] => 110001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => [3,2,1,7,6,5,4] => 110111
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => [3,2,1,6,7,5,4] => 110101
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => [3,2,1,5,7,6,4] => 110011
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => [3,2,1,6,5,7,4] => 110011
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => [3,2,1,5,6,7,4] => 110001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => [2,3,1,7,6,5,4] => 010111
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => [1,3,2,7,6,5,4] => 010111
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => [2,1,3,7,6,5,4] => 100111
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [1,2,3,7,6,5,4] => 000111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => [1,2,3,7,6,5,4] => 000111
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [1,2,3,6,7,5,4] => 000101
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => [1,2,3,7,6,5,4] => 000111
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => [1,2,3,6,7,5,4] => 000101
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => [1,2,3,5,7,6,4] => 000011
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => [1,2,3,5,7,6,4] => 000011
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => [1,2,3,6,5,7,4] => 000011
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => [1,2,3,5,6,7,4] => 000001
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => [1,2,3,7,6,5,4] => 000111
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => [1,2,3,6,7,5,4] => 000101
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => [1,2,3,5,7,6,4] => 000011
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [1,2,3,6,5,7,4] => 000011
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [1,2,3,5,6,7,4] => 000001
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [4,3,2,1,7,6,5] => 111011
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => [4,3,2,1,7,6,5] => 111011
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => [4,3,2,1,6,7,5] => 111001
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => [4,3,2,1,7,6,5] => 111011
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => [4,3,2,1,6,7,5] => 111001
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => [3,4,2,1,7,6,5] => 101011
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [3,4,2,1,7,6,5] => 101011
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => [3,4,2,1,6,7,5] => 101001
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => [3,4,2,1,7,6,5] => 101011
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => [3,4,2,1,6,7,5] => 101001
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => [2,4,3,1,7,6,5] => 011011
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => [2,4,3,1,7,6,5] => 011011
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => [2,4,3,1,6,7,5] => 011001
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => [2,4,3,1,7,6,5] => 011011
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => [2,4,3,1,6,7,5] => 011001
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [3,2,4,1,7,6,5] => 011011
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => [3,2,4,1,7,6,5] => 011011
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [3,2,4,1,6,7,5] => 011001
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [3,2,4,1,7,6,5] => 011011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => [3,2,4,1,6,7,5] => 011001
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => [2,3,4,1,7,6,5] => 001011
[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => [2,3,4,1,7,6,5] => 001011
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => [2,3,4,1,6,7,5] => 001001
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => [2,3,4,1,7,6,5] => 001011
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [2,3,4,1,6,7,5] => 001001
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => [1,4,3,2,7,6,5] => 011011
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [1,4,3,2,7,6,5] => 011011
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => [1,4,3,2,6,7,5] => 011001
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => [1,3,4,2,7,6,5] => 001011
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => [1,3,4,2,7,6,5] => 001011
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => [1,3,4,2,6,7,5] => 001001
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,5] => 101011
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [2,1,4,3,7,6,5] => 101011
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [2,1,4,3,6,7,5] => 101001
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [2,1,4,3,7,6,5] => 101011
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => [2,1,4,3,6,7,5] => 101001
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => [1,2,4,3,7,6,5] => 001011
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => [1,2,4,3,7,6,5] => 001011
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => [1,2,4,3,6,7,5] => 001001
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => [3,2,1,4,7,6,5] => 110011
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => [3,2,1,4,7,6,5] => 110011
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => [3,2,1,4,7,6,5] => 110011
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => [3,2,1,4,6,7,5] => 110001
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => [2,3,1,4,7,6,5] => 010011
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => [2,3,1,4,7,6,5] => 010011
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => [2,3,1,4,6,7,5] => 010001
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => [1,3,2,4,7,6,5] => 010011
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => [1,3,2,4,7,6,5] => 010011
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => [1,3,2,4,6,7,5] => 010001
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => [2,1,3,4,7,6,5] => 100011
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => [2,1,3,4,7,6,5] => 100011
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => [2,1,3,4,7,6,5] => 100011
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => [2,1,3,4,6,7,5] => 100001
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,5] => 000011
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => [1,2,3,4,7,6,5] => 000011
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [1,2,3,4,7,6,5] => 000011
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => [1,2,3,4,6,7,5] => 000001
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,7,6] => 111101
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => [5,4,3,2,1,7,6] => 111101
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => [4,5,3,2,1,7,6] => 110101
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [3,5,4,2,1,8,7,6] => [3,5,4,2,1,7,6] => 101101
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [4,3,5,2,1,8,7,6] => [4,3,5,2,1,7,6] => 101101
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => [3,4,5,2,1,7,6] => 100101
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [2,5,4,3,1,8,7,6] => [2,5,4,3,1,7,6] => 011101
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => [2,4,5,3,1,7,6] => 010101
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => [3,2,5,4,1,7,6] => 011101
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => [2,3,5,4,1,7,6] => 001101
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => [4,3,2,5,1,7,6] => 011101
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => [3,4,2,5,1,7,6] => 001101
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => [2,4,3,5,1,7,6] => 001101
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [3,2,4,5,1,8,7,6] => [3,2,4,5,1,7,6] => 010101
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => [2,3,4,5,1,7,6] => 000101
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,7,6] => 111001
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => [4,3,2,1,5,7,6] => 111001
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [3,2,4,1,5,7,6] => 011001
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => [3,2,4,1,5,7,6] => 011001
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => [2,3,4,1,5,7,6] => 001001
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => [2,3,4,1,5,7,6] => 001001
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,7,6] => 110001
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [2,3,1,4,5,7,6] => 010001
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,6] => 000001
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,7,6] => 000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,7] => 111110
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => [5,6,4,3,2,1,7] => 111010
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [4,5,6,3,2,1,7] => 110010
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => [3,6,5,4,2,1,7] => 101110
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => [4,3,6,5,2,1,7] => 101110
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [5,4,3,6,2,1,8,7] => [5,4,3,6,2,1,7] => 101110
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => [4,5,3,6,2,1,7] => 100110
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => [4,3,5,6,2,1,7] => 101010
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => [2,3,6,5,4,1,7] => 001110
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => [2,4,3,6,5,1,7] => 001110
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => [5,4,3,2,6,1,7] => 011110
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [4,5,3,2,6,1,8,7] => [4,5,3,2,6,1,7] => 010110
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [4,3,5,2,6,1,7] => 001110
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [3,2,5,4,6,1,7] => 010110
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => [4,3,2,5,6,1,7] => 011010
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => [2,3,4,5,6,1,7] => 000010
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => [1,5,6,4,3,2,7] => 011010
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,7] => 101110
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [2,1,5,6,4,3,7] => 101010
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => [2,1,4,6,5,3,7] => 100110
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [2,1,5,4,6,3,7] => 100110
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [2,1,4,5,6,3,7] => 100010
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,7] => 111010
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [3,4,2,1,6,5,7] => 101010
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => [2,4,3,1,6,5,7] => 011010
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [3,2,4,1,6,5,7] => 011010
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => [2,3,4,1,6,5,7] => 001010
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,7] => 101010
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,6,7] => 111100
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [2,1,5,4,3,6,8,7] => [2,1,5,4,3,6,7] => 101100
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,7] => 111000
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => [3,2,4,1,5,6,7] => 011000
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => [2,3,4,1,5,6,7] => 001000
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,7] => 100000
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [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
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => [5,7,6,4,3,2,1] => 111011
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [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
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => [4,7,6,5,3,2,1] => 110111
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1] => 110111
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => [3,4,7,6,5,2,1] => 100111
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => [3,2,7,6,5,4,1] => 011111
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => [3,2,6,7,5,4,1] => 011101
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => [5,4,3,2,7,6,1] => 011111
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => [4,5,3,2,7,6,1] => 010111
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => [3,5,4,2,7,6,1] => 001111
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => [3,2,5,4,7,6,1] => 010111
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => [2,3,4,5,7,6,1] => 000011
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [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
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [3,5,4,2,6,7,1,8] => [3,5,4,2,6,7,1] => 001101
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [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
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => [1,3,4,6,7,5,2] => 000101
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,3,4,5,7,6,2,8] => [1,3,4,5,7,6,2] => 000011
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => [2,1,6,7,5,4,3] => 101101
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => [2,3,1,5,6,7,4] => 010001
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5] => 111011
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => [4,3,2,1,6,7,5] => 111001
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => [3,2,4,1,7,6,5] => 011011
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => [3,2,4,1,6,7,5] => 011001
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => [2,3,4,1,7,6,5] => 001011
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => [2,3,4,1,6,7,5] => 001001
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5] => 011011
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [1,3,4,2,6,7,5] => 001001
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => [3,2,1,4,7,6,5] => 110011
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,7,6] => 111101
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => [3,2,1,5,4,7,6] => 110101
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [2,3,1,5,4,7,6] => 010101
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6] => 010101
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6] => 000101
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6] => 111001
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => [3,2,4,1,5,7,6] => 011001
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => [2,3,4,1,5,7,6] => 001001
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6] => 010001
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6] => 000001
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7] => 111110
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => [2,3,4,6,5,1,7] => 000110
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [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
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7] => 000010
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => [1,2,4,6,5,3,7] => 000110
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7] => 111010
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => [3,2,4,1,6,5,7] => 011010
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => [2,3,4,1,6,5,7] => 001010
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7] => 001010
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7] => 111100
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => [3,2,5,4,1,6,7] => 011100
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7] => 000100
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7] => 010100
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7] => 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
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7] => 110000
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7] => 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
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,2] => [1,3,4,5,6,7,8,2] => 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
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [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
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,9] => 10101010
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8] => 0000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9] => 00000000
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,1] => 0100001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,10] => 000000000
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [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
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,8,7] => 0000001
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,7,8,6] => 0000001
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,6,7,8,5] => 0000001
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,5,6,7,8,9,4] => [1,2,3,5,6,7,8,4] => 0000001
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,3] => [1,2,4,5,6,7,8,3] => 0000001
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,7] => 0000001
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,9,8] => 00000001
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,8,7,6] => 0000011
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,8,9,7] => 00000001
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,7,6,8,5] => 0000011
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,7,8,9,6] => 00000001
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [1,2,3,6,5,7,8,9,4] => [1,2,3,6,5,7,8,4] => 0000101
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,6,7,8,9,5] => 00000001
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [1,2,5,4,6,7,8,9,3] => [1,2,5,4,6,7,8,3] => 0001001
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,5,6,7,8,9,4] => 00000001
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,4,3,5,6,7,8,9,2] => [1,4,3,5,6,7,8,2] => 0010001
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,2,4,5,6,7,8,9,10,3] => [1,2,4,5,6,7,8,9,3] => 00000001
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,3,4,5,6,7,8,9,10,2] => [1,3,4,5,6,7,8,9,2] => 00000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [7,8,6,5,4,3,2,1] => 1111101
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0111111
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 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
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 0111111
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 01111111
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 011111111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => [2,1,9,8,7,6,5,4,3] => 10111111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => [4,3,2,1,9,8,7,6,5] => 11101111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,9,8,7] => 11111011
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,9] => 11111110
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [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
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.
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.