- FindStat

Identifier

Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St000392: Binary words ⟶ ℤ

Values

[[],[]] => [.,[.,.]] => [2,1] => 1 => 1

[[[]]] => [[.,.],.] => [1,2] => 0 => 0

[[],[],[]] => [.,[.,[.,.]]] => [3,2,1] => 11 => 2

[[],[[]]] => [.,[[.,.],.]] => [2,3,1] => 01 => 1

[[[]],[]] => [[.,.],[.,.]] => [1,3,2] => 01 => 1

[[[],[]]] => [[.,[.,.]],.] => [2,1,3] => 10 => 1

[[[[]]]] => [[[.,.],.],.] => [1,2,3] => 00 => 0

[[],[],[],[]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 111 => 3

[[],[],[[]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 011 => 2

[[],[[]],[]] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 011 => 2

[[],[[],[]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 101 => 1

[[],[[[]]]] => [.,[[[.,.],.],.]] => [2,3,4,1] => 001 => 1

[[[]],[],[]] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 011 => 2

[[[]],[[]]] => [[.,.],[[.,.],.]] => [1,3,4,2] => 001 => 1

[[[],[]],[]] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 101 => 1

[[[[]]],[]] => [[[.,.],.],[.,.]] => [1,2,4,3] => 001 => 1

[[[],[],[]]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 110 => 2

[[[],[[]]]] => [[.,[[.,.],.]],.] => [2,3,1,4] => 010 => 1

[[[[]],[]]] => [[[.,.],[.,.]],.] => [1,3,2,4] => 010 => 1

[[[[],[]]]] => [[[.,[.,.]],.],.] => [2,1,3,4] => 100 => 1

[[[[[]]]]] => [[[[.,.],.],.],.] => [1,2,3,4] => 000 => 0

[[],[],[],[],[]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1111 => 4

[[],[],[],[[]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 0111 => 3

[[],[],[[]],[]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 0111 => 3

[[],[],[[],[]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1011 => 2

[[],[],[[[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 0011 => 2

[[],[[]],[],[]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 0111 => 3

[[],[[]],[[]]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 0011 => 2

[[],[[],[]],[]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 1011 => 2

[[],[[[]]],[]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 0011 => 2

[[],[[],[],[]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1101 => 2

[[],[[],[[]]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 0101 => 1

[[],[[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 0101 => 1

[[],[[[],[]]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 1001 => 1

[[],[[[[]]]]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 0001 => 1

[[[]],[],[],[]] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 0111 => 3

[[[]],[],[[]]] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 0011 => 2

[[[]],[[]],[]] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 0011 => 2

[[[]],[[],[]]] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 0101 => 1

[[[]],[[[]]]] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 0001 => 1

[[[],[]],[],[]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1011 => 2

[[[[]]],[],[]] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 0011 => 2

[[[],[]],[[]]] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 1001 => 1

[[[[]]],[[]]] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 0001 => 1

[[[],[],[]],[]] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 1101 => 2

[[[],[[]]],[]] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 0101 => 1

[[[[]],[]],[]] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 0101 => 1

[[[[],[]]],[]] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 1001 => 1

[[[[[]]]],[]] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 0001 => 1

[[[],[],[],[]]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1110 => 3

[[[],[],[[]]]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 0110 => 2

[[[],[[]],[]]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 0110 => 2

[[[],[[],[]]]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 1010 => 1

[[[],[[[]]]]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 0010 => 1

[[[[]],[],[]]] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 0110 => 2

[[[[]],[[]]]] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 0010 => 1

[[[[],[]],[]]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 1010 => 1

[[[[[]]],[]]] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 0010 => 1

[[[[],[],[]]]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1100 => 2

[[[[],[[]]]]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 0100 => 1

[[[[[]],[]]]] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 0100 => 1

[[[[[],[]]]]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1000 => 1

[[[[[[]]]]]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0000 => 0

[[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 11111 => 5

[[],[],[],[],[[]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 01111 => 4

[[],[],[],[[]],[]] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 01111 => 4

[[],[],[],[[],[]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 10111 => 3

[[],[],[],[[[]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 00111 => 3

[[],[],[[]],[],[]] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 01111 => 4

[[],[],[[]],[[]]] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 00111 => 3

[[],[],[[],[]],[]] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 10111 => 3

[[],[],[[[]]],[]] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 00111 => 3

[[],[],[[],[],[]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 11011 => 2

[[],[],[[],[[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 01011 => 2

[[],[],[[[]],[]]] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 01011 => 2

[[],[],[[[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 10011 => 2

[[],[],[[[[]]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 00011 => 2

[[],[[]],[],[],[]] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 01111 => 4

[[],[[]],[],[[]]] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 00111 => 3

[[],[[]],[[]],[]] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 00111 => 3

[[],[[]],[[],[]]] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 01011 => 2

[[],[[]],[[[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 00011 => 2

[[],[[],[]],[],[]] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 10111 => 3

[[],[[[]]],[],[]] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 00111 => 3

[[],[[],[]],[[]]] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 10011 => 2

[[],[[[]]],[[]]] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 00011 => 2

[[],[[],[],[]],[]] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 11011 => 2

[[],[[],[[]]],[]] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 01011 => 2

[[],[[[]],[]],[]] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 01011 => 2

[[],[[[],[]]],[]] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 10011 => 2

[[],[[[[]]]],[]] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 00011 => 2

[[],[[],[],[],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 11101 => 3

[[],[[],[],[[]]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 01101 => 2

[[],[[],[[]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 01101 => 2

[[],[[],[[],[]]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 10101 => 1

[[],[[],[[[]]]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 00101 => 1

[[],[[[]],[],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 01101 => 2

[[],[[[]],[[]]]] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 00101 => 1

[[],[[[],[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 10101 => 1

[[],[[[[]]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 00101 => 1

[[],[[[],[],[]]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 11001 => 2

>>> Load all 1693 entries. <<<

[[],[[[],[[]]]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 01001 => 1

[[],[[[[]],[]]]] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 01001 => 1

[[],[[[[],[]]]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 10001 => 1

[[],[[[[[]]]]]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 00001 => 1

[[[]],[],[],[],[]] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 01111 => 4

[[[]],[],[],[[]]] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 00111 => 3

[[[]],[],[[]],[]] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 00111 => 3

[[[]],[],[[],[]]] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 01011 => 2

[[[]],[],[[[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 00011 => 2

[[[]],[[]],[],[]] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 00111 => 3

[[[]],[[]],[[]]] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 00011 => 2

[[[]],[[],[]],[]] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 01011 => 2

[[[]],[[[]]],[]] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 00011 => 2

[[[]],[[],[],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 01101 => 2

[[[]],[[],[[]]]] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 00101 => 1

[[[]],[[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 00101 => 1

[[[]],[[[],[]]]] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 01001 => 1

[[[]],[[[[]]]]] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 00001 => 1

[[[],[]],[],[],[]] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 10111 => 3

[[[[]]],[],[],[]] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 00111 => 3

[[[],[]],[],[[]]] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 10011 => 2

[[[[]]],[],[[]]] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 00011 => 2

[[[],[]],[[]],[]] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 10011 => 2

[[[[]]],[[]],[]] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 00011 => 2

[[[],[]],[[],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 10101 => 1

[[[],[]],[[[]]]] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 10001 => 1

[[[[]]],[[],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 00101 => 1

[[[[]]],[[[]]]] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 00001 => 1

[[[],[],[]],[],[]] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 11011 => 2

[[[],[[]]],[],[]] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 01011 => 2

[[[[]],[]],[],[]] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 01011 => 2

[[[[],[]]],[],[]] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 10011 => 2

[[[[[]]]],[],[]] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 00011 => 2

[[[],[],[]],[[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 11001 => 2

[[[],[[]]],[[]]] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 01001 => 1

[[[[]],[]],[[]]] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 01001 => 1

[[[[],[]]],[[]]] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 10001 => 1

[[[[[]]]],[[]]] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 00001 => 1

[[[],[],[],[]],[]] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 11101 => 3

[[[],[],[[]]],[]] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 01101 => 2

[[[],[[]],[]],[]] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 01101 => 2

[[[],[[],[]]],[]] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 10101 => 1

[[[],[[[]]]],[]] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 00101 => 1

[[[[]],[],[]],[]] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 01101 => 2

[[[[]],[[]]],[]] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 00101 => 1

[[[[],[]],[]],[]] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 10101 => 1

[[[[[]]],[]],[]] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 00101 => 1

[[[[],[],[]]],[]] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 11001 => 2

[[[[],[[]]]],[]] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 01001 => 1

[[[[[]],[]]],[]] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 01001 => 1

[[[[[],[]]]],[]] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 10001 => 1

[[[[[[]]]]],[]] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 00001 => 1

[[[],[],[],[],[]]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 11110 => 4

[[[],[],[],[[]]]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 01110 => 3

[[[],[],[[]],[]]] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 01110 => 3

[[[],[],[[],[]]]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 10110 => 2

[[[],[],[[[]]]]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 00110 => 2

[[[],[[]],[],[]]] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 01110 => 3

[[[],[[]],[[]]]] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 00110 => 2

[[[],[[],[]],[]]] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 10110 => 2

[[[],[[[]]],[]]] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 00110 => 2

[[[],[[],[],[]]]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 11010 => 2

[[[],[[],[[]]]]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 01010 => 1

[[[],[[[]],[]]]] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 01010 => 1

[[[],[[[],[]]]]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 10010 => 1

[[[],[[[[]]]]]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 00010 => 1

[[[[]],[],[],[]]] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 01110 => 3

[[[[]],[],[[]]]] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 00110 => 2

[[[[]],[[]],[]]] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 00110 => 2

[[[[]],[[],[]]]] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 01010 => 1

[[[[]],[[[]]]]] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 00010 => 1

[[[[],[]],[],[]]] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 10110 => 2

[[[[[]]],[],[]]] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 00110 => 2

[[[[],[]],[[]]]] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 10010 => 1

[[[[[]]],[[]]]] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 00010 => 1

[[[[],[],[]],[]]] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 11010 => 2

[[[[],[[]]],[]]] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 01010 => 1

[[[[[]],[]],[]]] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 01010 => 1

[[[[[],[]]],[]]] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 10010 => 1

[[[[[[]]]],[]]] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 00010 => 1

[[[[],[],[],[]]]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 11100 => 3

[[[[],[],[[]]]]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 01100 => 2

[[[[],[[]],[]]]] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 01100 => 2

[[[[],[[],[]]]]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 10100 => 1

[[[[],[[[]]]]]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 00100 => 1

[[[[[]],[],[]]]] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 01100 => 2

[[[[[]],[[]]]]] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 00100 => 1

[[[[[],[]],[]]]] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 10100 => 1

[[[[[[]]],[]]]] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 00100 => 1

[[[[[],[],[]]]]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 11000 => 2

[[[[[],[[]]]]]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 01000 => 1

[[[[[[]],[]]]]] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 01000 => 1

[[[[[[],[]]]]]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 10000 => 1

[[[[[[[]]]]]]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 00000 => 0

[[],[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 111111 => 6

[[],[],[],[],[],[[]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => 011111 => 5

[[],[],[],[],[[]],[]] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => 011111 => 5

[[],[],[],[],[[],[]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => 101111 => 4

[[],[],[],[],[[[]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => 001111 => 4

[[],[],[],[[]],[],[]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => 011111 => 5

[[],[],[],[[]],[[]]] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => 001111 => 4

[[],[],[],[[],[]],[]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => 101111 => 4

[[],[],[],[[[]]],[]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => 001111 => 4

[[],[],[],[[],[],[]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => 110111 => 3

[[],[],[],[[],[[]]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => 010111 => 3

[[],[],[],[[[]],[]]] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => 010111 => 3

[[],[],[],[[[],[]]]] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => 100111 => 3

[[],[],[],[[[[]]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => 000111 => 3

[[],[],[[]],[],[],[]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => 011111 => 5

[[],[],[[]],[],[[]]] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => 001111 => 4

[[],[],[[]],[[]],[]] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => 001111 => 4

[[],[],[[]],[[],[]]] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => 010111 => 3

[[],[],[[]],[[[]]]] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => 000111 => 3

[[],[],[[],[]],[],[]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => 101111 => 4

[[],[],[[[]]],[],[]] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => 001111 => 4

[[],[],[[],[]],[[]]] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => 100111 => 3

[[],[],[[[]]],[[]]] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => 000111 => 3

[[],[],[[],[],[]],[]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => 110111 => 3

[[],[],[[],[[]]],[]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => 010111 => 3

[[],[],[[[]],[]],[]] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => 010111 => 3

[[],[],[[[],[]]],[]] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => 100111 => 3

[[],[],[[[[]]]],[]] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => 000111 => 3

[[],[],[[],[],[],[]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => 111011 => 3

[[],[],[[],[],[[]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => 011011 => 2

[[],[],[[],[[]],[]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => 011011 => 2

[[],[],[[],[[],[]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => 101011 => 2

[[],[],[[],[[[]]]]] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => 001011 => 2

[[],[],[[[]],[],[]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => 011011 => 2

[[],[],[[[]],[[]]]] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => 001011 => 2

[[],[],[[[],[]],[]]] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => 101011 => 2

[[],[],[[[[]]],[]]] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => 001011 => 2

[[],[],[[[],[],[]]]] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => 110011 => 2

[[],[],[[[],[[]]]]] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => 010011 => 2

[[],[],[[[[]],[]]]] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => 010011 => 2

[[],[],[[[[],[]]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => 100011 => 2

[[],[],[[[[[]]]]]] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => 000011 => 2

[[],[[]],[],[],[],[]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => 011111 => 5

[[],[[]],[],[],[[]]] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => 001111 => 4

[[],[[]],[],[[]],[]] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => 001111 => 4

[[],[[]],[],[[],[]]] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => 010111 => 3

[[],[[]],[],[[[]]]] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => 000111 => 3

[[],[[]],[[]],[],[]] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => 001111 => 4

[[],[[]],[[]],[[]]] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => 000111 => 3

[[],[[]],[[],[]],[]] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => 010111 => 3

[[],[[]],[[[]]],[]] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => 000111 => 3

[[],[[]],[[],[],[]]] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => 011011 => 2

[[],[[]],[[],[[]]]] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => 001011 => 2

[[],[[]],[[[]],[]]] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => 001011 => 2

[[],[[]],[[[],[]]]] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => 010011 => 2

[[],[[]],[[[[]]]]] => [.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => 000011 => 2

[[],[[],[]],[],[],[]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => 101111 => 4

[[],[[[]]],[],[],[]] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => 001111 => 4

[[],[[],[]],[],[[]]] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => 100111 => 3

[[],[[[]]],[],[[]]] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => 000111 => 3

[[],[[],[]],[[]],[]] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => 100111 => 3

[[],[[[]]],[[]],[]] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => 000111 => 3

[[],[[],[]],[[],[]]] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => 101011 => 2

[[],[[],[]],[[[]]]] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => 100011 => 2

[[],[[[]]],[[],[]]] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => 001011 => 2

[[],[[[]]],[[[]]]] => [.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => 000011 => 2

[[],[[],[],[]],[],[]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => 110111 => 3

[[],[[],[[]]],[],[]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => 010111 => 3

[[],[[[]],[]],[],[]] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => 010111 => 3

[[],[[[],[]]],[],[]] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => 100111 => 3

[[],[[[[]]]],[],[]] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => 000111 => 3

[[],[[],[],[]],[[]]] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => 110011 => 2

[[],[[],[[]]],[[]]] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => 010011 => 2

[[],[[[]],[]],[[]]] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => 010011 => 2

[[],[[[],[]]],[[]]] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => 100011 => 2

[[],[[[[]]]],[[]]] => [.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => 000011 => 2

[[],[[],[],[],[]],[]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => 111011 => 3

[[],[[],[],[[]]],[]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => 011011 => 2

[[],[[],[[]],[]],[]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => 011011 => 2

[[],[[],[[],[]]],[]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => 101011 => 2

[[],[[],[[[]]]],[]] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => 001011 => 2

[[],[[[]],[],[]],[]] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => 011011 => 2

[[],[[[]],[[]]],[]] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => 001011 => 2

[[],[[[],[]],[]],[]] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => 101011 => 2

[[],[[[[]]],[]],[]] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => 001011 => 2

[[],[[[],[],[]]],[]] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => 110011 => 2

[[],[[[],[[]]]],[]] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => 010011 => 2

[[],[[[[]],[]]],[]] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => 010011 => 2

[[],[[[[],[]]]],[]] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => 100011 => 2

[[],[[[[[]]]]],[]] => [.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => 000011 => 2

[[],[[],[],[],[],[]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => 111101 => 4

[[],[[],[],[],[[]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => 011101 => 3

[[],[[],[],[[]],[]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => 011101 => 3

[[],[[],[],[[],[]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => 101101 => 2

[[],[[],[],[[[]]]]] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => 001101 => 2

[[],[[],[[]],[],[]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => 011101 => 3

[[],[[],[[]],[[]]]] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => 001101 => 2

[[],[[],[[],[]],[]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => 101101 => 2

[[],[[],[[[]]],[]]] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => 001101 => 2

[[],[[],[[],[],[]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => 110101 => 2

[[],[[],[[],[[]]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => 010101 => 1

[[],[[],[[[]],[]]]] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => 010101 => 1

[[],[[],[[[],[]]]]] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => 100101 => 1

[[],[[],[[[[]]]]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 000101 => 1

[[],[[[]],[],[],[]]] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => 011101 => 3

[[],[[[]],[],[[]]]] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => 001101 => 2

[[],[[[]],[[]],[]]] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => 001101 => 2

[[],[[[]],[[],[]]]] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => 010101 => 1

[[],[[[]],[[[]]]]] => [.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => 000101 => 1

[[],[[[],[]],[],[]]] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => 101101 => 2

[[],[[[[]]],[],[]]] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => 001101 => 2

[[],[[[],[]],[[]]]] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => 100101 => 1

[[],[[[[]]],[[]]]] => [.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => 000101 => 1

[[],[[[],[],[]],[]]] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => 110101 => 2

[[],[[[],[[]]],[]]] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => 010101 => 1

[[],[[[[]],[]],[]]] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => 010101 => 1

[[],[[[[],[]]],[]]] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => 100101 => 1

[[],[[[[[]]]],[]]] => [.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => 000101 => 1

[[],[[[],[],[],[]]]] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => 111001 => 3

[[],[[[],[],[[]]]]] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => 011001 => 2

[[],[[[],[[]],[]]]] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => 011001 => 2

[[],[[[],[[],[]]]]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 101001 => 1

[[],[[[],[[[]]]]]] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 001001 => 1

[[],[[[[]],[],[]]]] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => 011001 => 2

[[],[[[[]],[[]]]]] => [.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => 001001 => 1

[[],[[[[],[]],[]]]] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => 101001 => 1

[[],[[[[[]]],[]]]] => [.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => 001001 => 1

[[],[[[[],[],[]]]]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 110001 => 2

[[],[[[[],[[]]]]]] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 010001 => 1

[[],[[[[[]],[]]]]] => [.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => 010001 => 1

[[],[[[[[],[]]]]]] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 100001 => 1

[[],[[[[[[]]]]]]] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 000001 => 1

[[[]],[],[],[],[],[]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 011111 => 5

[[[]],[],[],[],[[]]] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 001111 => 4

[[[]],[],[],[[]],[]] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 001111 => 4

[[[]],[],[],[[],[]]] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 010111 => 3

[[[]],[],[],[[[]]]] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 000111 => 3

[[[]],[],[[]],[],[]] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 001111 => 4

[[[]],[],[[]],[[]]] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 000111 => 3

[[[]],[],[[],[]],[]] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 010111 => 3

[[[]],[],[[[]]],[]] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => 000111 => 3

[[[]],[],[[],[],[]]] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 011011 => 2

[[[]],[],[[],[[]]]] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 001011 => 2

[[[]],[],[[[]],[]]] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => 001011 => 2

[[[]],[],[[[],[]]]] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => 010011 => 2

[[[]],[],[[[[]]]]] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => 000011 => 2

[[[]],[[]],[],[],[]] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 001111 => 4

[[[]],[[]],[],[[]]] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 000111 => 3

[[[]],[[]],[[]],[]] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 000111 => 3

[[[]],[[]],[[],[]]] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 001011 => 2

[[[]],[[]],[[[]]]] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => 000011 => 2

[[[]],[[],[]],[],[]] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 010111 => 3

[[[]],[[[]]],[],[]] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => 000111 => 3

[[[]],[[],[]],[[]]] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 010011 => 2

[[[]],[[[]]],[[]]] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => 000011 => 2

[[[]],[[],[],[]],[]] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => 011011 => 2

[[[]],[[],[[]]],[]] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => 001011 => 2

[[[]],[[[]],[]],[]] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => 001011 => 2

[[[]],[[[],[]]],[]] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => 010011 => 2

[[[]],[[[[]]]],[]] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => 000011 => 2

[[[]],[[],[],[],[]]] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 011101 => 3

[[[]],[[],[],[[]]]] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => 001101 => 2

[[[]],[[],[[]],[]]] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => 001101 => 2

[[[]],[[],[[],[]]]] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => 010101 => 1

[[[]],[[],[[[]]]]] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => 000101 => 1

[[[]],[[[]],[],[]]] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => 001101 => 2

[[[]],[[[]],[[]]]] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => 000101 => 1

[[[]],[[[],[]],[]]] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => 010101 => 1

[[[]],[[[[]]],[]]] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => 000101 => 1

[[[]],[[[],[],[]]]] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => 011001 => 2

[[[]],[[[],[[]]]]] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => 001001 => 1

[[[]],[[[[]],[]]]] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => 001001 => 1

[[[]],[[[[],[]]]]] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => 010001 => 1

[[[]],[[[[[]]]]]] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => 000001 => 1

[[[],[]],[],[],[],[]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 101111 => 4

[[[[]]],[],[],[],[]] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => 001111 => 4

[[[],[]],[],[],[[]]] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => 100111 => 3

[[[[]]],[],[],[[]]] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => 000111 => 3

[[[],[]],[],[[]],[]] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => 100111 => 3

[[[[]]],[],[[]],[]] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => 000111 => 3

[[[],[]],[],[[],[]]] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => 101011 => 2

[[[],[]],[],[[[]]]] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => 100011 => 2

[[[[]]],[],[[],[]]] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => 001011 => 2

[[[[]]],[],[[[]]]] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => 000011 => 2

[[[],[]],[[]],[],[]] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => 100111 => 3

[[[[]]],[[]],[],[]] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => 000111 => 3

[[[],[]],[[]],[[]]] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => 100011 => 2

[[[[]]],[[]],[[]]] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => 000011 => 2

[[[],[]],[[],[]],[]] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => 101011 => 2

[[[],[]],[[[]]],[]] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => 100011 => 2

[[[[]]],[[],[]],[]] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => 001011 => 2

[[[[]]],[[[]]],[]] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => 000011 => 2

[[[],[]],[[],[],[]]] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => 101101 => 2

[[[],[]],[[],[[]]]] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => 100101 => 1

[[[],[]],[[[]],[]]] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => 100101 => 1

[[[],[]],[[[],[]]]] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => 101001 => 1

[[[],[]],[[[[]]]]] => [[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => 100001 => 1

[[[[]]],[[],[],[]]] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => 001101 => 2

[[[[]]],[[],[[]]]] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => 000101 => 1

[[[[]]],[[[]],[]]] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => 000101 => 1

[[[[]]],[[[],[]]]] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => 001001 => 1

[[[[]]],[[[[]]]]] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => 000001 => 1

[[[],[],[]],[],[],[]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => 110111 => 3

[[[],[[]]],[],[],[]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => 010111 => 3

[[[[]],[]],[],[],[]] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => 010111 => 3

[[[[],[]]],[],[],[]] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => 100111 => 3

[[[[[]]]],[],[],[]] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => 000111 => 3

[[[],[],[]],[],[[]]] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => 110011 => 2

[[[],[[]]],[],[[]]] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => 010011 => 2

[[[[]],[]],[],[[]]] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => 010011 => 2

[[[[],[]]],[],[[]]] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => 100011 => 2

[[[[[]]]],[],[[]]] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => 000011 => 2

[[[],[],[]],[[]],[]] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => 110011 => 2

[[[],[[]]],[[]],[]] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => 010011 => 2

[[[[]],[]],[[]],[]] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 010011 => 2

[[[[],[]]],[[]],[]] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => 100011 => 2

[[[[[]]]],[[]],[]] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => 000011 => 2

[[[],[],[]],[[],[]]] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => 110101 => 2

[[[],[],[]],[[[]]]] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => 110001 => 2

[[[],[[]]],[[],[]]] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => 010101 => 1

[[[],[[]]],[[[]]]] => [[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => 010001 => 1

[[[[]],[]],[[],[]]] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => 010101 => 1

[[[[]],[]],[[[]]]] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => 010001 => 1

[[[[],[]]],[[],[]]] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => 100101 => 1

[[[[],[]]],[[[]]]] => [[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => 100001 => 1

[[[[[]]]],[[],[]]] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => 000101 => 1

[[[[[]]]],[[[]]]] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => 000001 => 1

[[[],[],[],[]],[],[]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => 111011 => 3

[[[],[],[[]]],[],[]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => 011011 => 2

[[[],[[]],[]],[],[]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => 011011 => 2

[[[],[[],[]]],[],[]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => 101011 => 2

[[[],[[[]]]],[],[]] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => 001011 => 2

[[[[]],[],[]],[],[]] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 011011 => 2

[[[[]],[[]]],[],[]] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => 001011 => 2

[[[[],[]],[]],[],[]] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => 101011 => 2

[[[[[]]],[]],[],[]] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => 001011 => 2

[[[[],[],[]]],[],[]] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => 110011 => 2

[[[[],[[]]]],[],[]] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => 010011 => 2

[[[[[]],[]]],[],[]] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => 010011 => 2

[[[[[],[]]]],[],[]] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => 100011 => 2

[[[[[[]]]]],[],[]] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => 000011 => 2

[[[],[],[],[]],[[]]] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => 111001 => 3

[[[],[],[[]]],[[]]] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => 011001 => 2

[[[],[[]],[]],[[]]] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => 011001 => 2

[[[],[[],[]]],[[]]] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => 101001 => 1

[[[],[[[]]]],[[]]] => [[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => 001001 => 1

[[[[]],[],[]],[[]]] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => 011001 => 2

[[[[]],[[]]],[[]]] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => 001001 => 1

[[[[],[]],[]],[[]]] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => 101001 => 1

[[[[[]]],[]],[[]]] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => 001001 => 1

[[[[],[],[]]],[[]]] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => 110001 => 2

[[[[],[[]]]],[[]]] => [[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => 010001 => 1

[[[[[]],[]]],[[]]] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => 010001 => 1

[[[[[],[]]]],[[]]] => [[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => 100001 => 1

[[[[[[]]]]],[[]]] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => 000001 => 1

[[[],[],[],[],[]],[]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => 111101 => 4

[[[],[],[],[[]]],[]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => 011101 => 3

[[[],[],[[]],[]],[]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => 011101 => 3

[[[],[],[[],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => 101101 => 2

[[[],[],[[[]]]],[]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => 001101 => 2

[[[],[[]],[],[]],[]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => 011101 => 3

[[[],[[]],[[]]],[]] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => 001101 => 2

[[[],[[],[]],[]],[]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => 101101 => 2

[[[],[[[]]],[]],[]] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => 001101 => 2

[[[],[[],[],[]]],[]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => 110101 => 2

[[[],[[],[[]]]],[]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => 010101 => 1

[[[],[[[]],[]]],[]] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => 010101 => 1

[[[],[[[],[]]]],[]] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => 100101 => 1

[[[],[[[[]]]]],[]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => 000101 => 1

[[[[]],[],[],[]],[]] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => 011101 => 3

[[[[]],[],[[]]],[]] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => 001101 => 2

[[[[]],[[]],[]],[]] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => 001101 => 2

[[[[]],[[],[]]],[]] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => 010101 => 1

[[[[]],[[[]]]],[]] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => 000101 => 1

[[[[],[]],[],[]],[]] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => 101101 => 2

[[[[[]]],[],[]],[]] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => 001101 => 2

[[[[],[]],[[]]],[]] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => 100101 => 1

[[[[[]]],[[]]],[]] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => 000101 => 1

[[[[],[],[]],[]],[]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => 110101 => 2

[[[[],[[]]],[]],[]] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => 010101 => 1

[[[[[]],[]],[]],[]] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 010101 => 1

[[[[[],[]]],[]],[]] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => 100101 => 1

[[[[[[]]]],[]],[]] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => 000101 => 1

[[[[],[],[],[]]],[]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => 111001 => 3

[[[[],[],[[]]]],[]] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => 011001 => 2

[[[[],[[]],[]]],[]] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => 011001 => 2

[[[[],[[],[]]]],[]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => 101001 => 1

[[[[],[[[]]]]],[]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => 001001 => 1

[[[[[]],[],[]]],[]] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => 011001 => 2

[[[[[]],[[]]]],[]] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => 001001 => 1

[[[[[],[]],[]]],[]] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => 101001 => 1

[[[[[[]]],[]]],[]] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => 001001 => 1

[[[[[],[],[]]]],[]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => 110001 => 2

[[[[[],[[]]]]],[]] => [[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => 010001 => 1

[[[[[[]],[]]]],[]] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => 010001 => 1

[[[[[[],[]]]]],[]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => 100001 => 1

[[[[[[[]]]]]],[]] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 000001 => 1

[[[],[],[],[],[],[]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 111110 => 5

[[[],[],[],[],[[]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 011110 => 4

[[[],[],[],[[]],[]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 011110 => 4

[[[],[],[],[[],[]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 101110 => 3

[[[],[],[],[[[]]]]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 001110 => 3

[[[],[],[[]],[],[]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 011110 => 4

[[[],[],[[]],[[]]]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 001110 => 3

[[[],[],[[],[]],[]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 101110 => 3

[[[],[],[[[]]],[]]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => 001110 => 3

[[[],[],[[],[],[]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 110110 => 2

[[[],[],[[],[[]]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 010110 => 2

[[[],[],[[[]],[]]]] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => 010110 => 2

[[[],[],[[[],[]]]]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => 100110 => 2

[[[],[],[[[[]]]]]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => 000110 => 2

[[[],[[]],[],[],[]]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 011110 => 4

[[[],[[]],[],[[]]]] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => 001110 => 3

[[[],[[]],[[]],[]]] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => 001110 => 3

[[[],[[]],[[],[]]]] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => 010110 => 2

[[[],[[]],[[[]]]]] => [[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => 000110 => 2

[[[],[[],[]],[],[]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => 101110 => 3

[[[],[[[]]],[],[]]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => 001110 => 3

[[[],[[],[]],[[]]]] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => 100110 => 2

[[[],[[[]]],[[]]]] => [[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => 000110 => 2

[[[],[[],[],[]],[]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => 110110 => 2

[[[],[[],[[]]],[]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => 010110 => 2

[[[],[[[]],[]],[]]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => 010110 => 2

[[[],[[[],[]]],[]]] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => 100110 => 2

[[[],[[[[]]]],[]]] => [[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => 000110 => 2

[[[],[[],[],[],[]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 111010 => 3

[[[],[[],[],[[]]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => 011010 => 2

[[[],[[],[[]],[]]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => 011010 => 2

[[[],[[],[[],[]]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => 101010 => 1

[[[],[[],[[[]]]]]] => [[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => 001010 => 1

[[[],[[[]],[],[]]]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => 011010 => 2

[[[],[[[]],[[]]]]] => [[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => 001010 => 1

[[[],[[[],[]],[]]]] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => 101010 => 1

[[[],[[[[]]],[]]]] => [[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => 001010 => 1

[[[],[[[],[],[]]]]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => 110010 => 2

[[[],[[[],[[]]]]]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => 010010 => 1

[[[],[[[[]],[]]]]] => [[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => 010010 => 1

[[[],[[[[],[]]]]]] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => 100010 => 1

[[[],[[[[[]]]]]]] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 000010 => 1

[[[[]],[],[],[],[]]] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => 011110 => 4

[[[[]],[],[],[[]]]] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => 001110 => 3

[[[[]],[],[[]],[]]] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => 001110 => 3

[[[[]],[],[[],[]]]] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => 010110 => 2

[[[[]],[],[[[]]]]] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => 000110 => 2

[[[[]],[[]],[],[]]] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => 001110 => 3

[[[[]],[[]],[[]]]] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => 000110 => 2

[[[[]],[[],[]],[]]] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => 010110 => 2

[[[[]],[[[]]],[]]] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => 000110 => 2

[[[[]],[[],[],[]]]] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => 011010 => 2

[[[[]],[[],[[]]]]] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => 001010 => 1

[[[[]],[[[]],[]]]] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => 001010 => 1

[[[[]],[[[],[]]]]] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => 010010 => 1

[[[[]],[[[[]]]]]] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => 000010 => 1

[[[[],[]],[],[],[]]] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => 101110 => 3

[[[[[]]],[],[],[]]] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => 001110 => 3

[[[[],[]],[],[[]]]] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => 100110 => 2

[[[[[]]],[],[[]]]] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => 000110 => 2

[[[[],[]],[[]],[]]] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => 100110 => 2

[[[[[]]],[[]],[]]] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => 000110 => 2

[[[[],[]],[[],[]]]] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => 101010 => 1

[[[[],[]],[[[]]]]] => [[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => 100010 => 1

[[[[[]]],[[],[]]]] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => 001010 => 1

[[[[[]]],[[[]]]]] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => 000010 => 1

[[[[],[],[]],[],[]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => 110110 => 2

[[[[],[[]]],[],[]]] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => 010110 => 2

[[[[[]],[]],[],[]]] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => 010110 => 2

[[[[[],[]]],[],[]]] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => 100110 => 2

[[[[[[]]]],[],[]]] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => 000110 => 2

[[[[],[],[]],[[]]]] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => 110010 => 2

[[[[],[[]]],[[]]]] => [[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => 010010 => 1

[[[[[]],[]],[[]]]] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => 010010 => 1

[[[[[],[]]],[[]]]] => [[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => 100010 => 1

[[[[[[]]]],[[]]]] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => 000010 => 1

[[[[],[],[],[]],[]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => 111010 => 3

[[[[],[],[[]]],[]]] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => 011010 => 2

[[[[],[[]],[]],[]]] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => 011010 => 2

[[[[],[[],[]]],[]]] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => 101010 => 1

[[[[],[[[]]]],[]]] => [[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => 001010 => 1

[[[[[]],[],[]],[]]] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => 011010 => 2

[[[[[]],[[]]],[]]] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => 001010 => 1

[[[[[],[]],[]],[]]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => 101010 => 1

[[[[[[]]],[]],[]]] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => 001010 => 1

[[[[[],[],[]]],[]]] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => 110010 => 2

[[[[[],[[]]]],[]]] => [[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => 010010 => 1

[[[[[[]],[]]],[]]] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => 010010 => 1

[[[[[[],[]]]],[]]] => [[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => 100010 => 1

[[[[[[[]]]]],[]]] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 000010 => 1

[[[[],[],[],[],[]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 111100 => 4

[[[[],[],[],[[]]]]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => 011100 => 3

[[[[],[],[[]],[]]]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => 011100 => 3

[[[[],[],[[],[]]]]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => 101100 => 2

[[[[],[],[[[]]]]]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => 001100 => 2

[[[[],[[]],[],[]]]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => 011100 => 3

[[[[],[[]],[[]]]]] => [[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => 001100 => 2

[[[[],[[],[]],[]]]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => 101100 => 2

[[[[],[[[]]],[]]]] => [[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => 001100 => 2

[[[[],[[],[],[]]]]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => 110100 => 2

[[[[],[[],[[]]]]]] => [[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => 010100 => 1

[[[[],[[[]],[]]]]] => [[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => 010100 => 1

[[[[],[[[],[]]]]]] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => 100100 => 1

[[[[],[[[[]]]]]]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 000100 => 1

[[[[[]],[],[],[]]]] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => 011100 => 3

[[[[[]],[],[[]]]]] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => 001100 => 2

[[[[[]],[[]],[]]]] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => 001100 => 2

[[[[[]],[[],[]]]]] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => 010100 => 1

[[[[[]],[[[]]]]]] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => 000100 => 1

[[[[[],[]],[],[]]]] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => 101100 => 2

[[[[[[]]],[],[]]]] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => 001100 => 2

[[[[[],[]],[[]]]]] => [[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => 100100 => 1

[[[[[[]]],[[]]]]] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => 000100 => 1

[[[[[],[],[]],[]]]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => 110100 => 2

[[[[[],[[]]],[]]]] => [[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => 010100 => 1

[[[[[[]],[]],[]]]] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => 010100 => 1

[[[[[[],[]]],[]]]] => [[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => 100100 => 1

[[[[[[[]]]],[]]]] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => 000100 => 1

[[[[[],[],[],[]]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 111000 => 3

[[[[[],[],[[]]]]]] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => 011000 => 2

[[[[[],[[]],[]]]]] => [[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => 011000 => 2

[[[[[],[[],[]]]]]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => 101000 => 1

[[[[[],[[[]]]]]]] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 001000 => 1

[[[[[[]],[],[]]]]] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => 011000 => 2

[[[[[[]],[[]]]]]] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => 001000 => 1

[[[[[[],[]],[]]]]] => [[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => 101000 => 1

[[[[[[[]]],[]]]]] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => 001000 => 1

[[[[[[],[],[]]]]]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 110000 => 2

[[[[[[],[[]]]]]]] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 010000 => 1

[[[[[[[]],[]]]]]] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 010000 => 1

[[[[[[[],[]]]]]]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 100000 => 1

[[[[[[[[]]]]]]]] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 000000 => 0

[[],[],[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 1111111 => 7

[[],[],[],[],[],[],[[]]] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => 0111111 => 6

[[],[],[],[],[],[[]],[]] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [6,8,7,5,4,3,2,1] => 0111111 => 6

[[],[],[],[],[],[[],[]]] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 1011111 => 5

[[],[],[],[],[],[[[]]]] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => 0011111 => 5

[[],[],[],[],[[]],[],[]] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [5,8,7,6,4,3,2,1] => 0111111 => 6

[[],[],[],[],[[]],[[]]] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [5,7,8,6,4,3,2,1] => 0011111 => 5

[[],[],[],[],[[],[]],[]] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 1011111 => 5

[[],[],[],[],[[[]]],[]] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [5,6,8,7,4,3,2,1] => 0011111 => 5

[[],[],[],[],[[],[],[]]] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => 1101111 => 4

[[],[],[],[],[[],[[]]]] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => 0101111 => 4

[[],[],[],[],[[[]],[]]] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => 0101111 => 4

[[],[],[],[],[[[],[]]]] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => 1001111 => 4

[[],[],[],[],[[[[]]]]] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => 0001111 => 4

[[],[],[],[[]],[],[],[]] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [4,8,7,6,5,3,2,1] => 0111111 => 6

[[],[],[],[[]],[],[[]]] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [4,7,8,6,5,3,2,1] => 0011111 => 5

[[],[],[],[[]],[[]],[]] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => 0011111 => 5

[[],[],[],[[]],[[],[]]] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [4,7,6,8,5,3,2,1] => 0101111 => 4

[[],[],[],[[]],[[[]]]] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [4,6,7,8,5,3,2,1] => 0001111 => 4

[[],[],[],[[[]]],[],[]] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [4,5,8,7,6,3,2,1] => 0011111 => 5

[[],[],[],[[],[]],[[]]] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [5,4,7,8,6,3,2,1] => 1001111 => 4

[[],[],[],[[[]]],[[]]] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [4,5,7,8,6,3,2,1] => 0001111 => 4

[[],[],[],[[],[],[]],[]] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [6,5,4,8,7,3,2,1] => 1101111 => 4

[[],[],[],[[],[[]]],[]] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [5,6,4,8,7,3,2,1] => 0101111 => 4

[[],[],[],[[[]],[]],[]] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [4,6,5,8,7,3,2,1] => 0101111 => 4

[[],[],[],[[[[]]]],[]] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => 0001111 => 4

[[],[],[],[[],[],[],[]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 1110111 => 3

[[],[],[],[[],[],[[]]]] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => 0110111 => 3

[[],[],[],[[],[[]],[]]] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [5,7,6,4,8,3,2,1] => 0110111 => 3

[[],[],[],[[],[[],[]]]] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 1010111 => 3

[[],[],[],[[],[[[]]]]] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => 0010111 => 3

[[],[],[],[[[]],[],[]]] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1] => 0110111 => 3

[[],[],[],[[[]],[[]]]] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [4,6,7,5,8,3,2,1] => 0010111 => 3

[[],[],[],[[[],[]],[]]] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1] => 1010111 => 3

[[],[],[],[[[[]]],[]]] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1] => 0010111 => 3

[[],[],[],[[[],[],[]]]] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => 1100111 => 3

[[],[],[],[[[],[[]]]]] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => 0100111 => 3

[[],[],[],[[[[]],[]]]] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [4,6,5,7,8,3,2,1] => 0100111 => 3

[[],[],[],[[[[],[]]]]] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => 1000111 => 3

[[],[],[],[[[[[]]]]]] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => 0000111 => 3

[[],[],[[]],[],[],[],[]] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [3,8,7,6,5,4,2,1] => 0111111 => 6

[[],[],[[]],[],[],[[]]] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => 0011111 => 5

[[],[],[[]],[],[[]],[]] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [3,6,8,7,5,4,2,1] => 0011111 => 5

[[],[],[[]],[],[[],[]]] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [3,7,6,8,5,4,2,1] => 0101111 => 4

[[],[],[[]],[[]],[],[]] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => 0011111 => 5

[[],[],[[]],[[]],[[]]] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => 0001111 => 4

[[],[],[[]],[[[]]],[]] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [3,5,6,8,7,4,2,1] => 0001111 => 4

[[],[],[[]],[[],[],[]]] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [3,7,6,5,8,4,2,1] => 0110111 => 3

[[],[],[[]],[[],[[]]]] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [3,6,7,5,8,4,2,1] => 0010111 => 3

[[],[],[[]],[[[]],[]]] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [3,5,7,6,8,4,2,1] => 0010111 => 3

[[],[],[[]],[[[[]]]]] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [3,5,6,7,8,4,2,1] => 0000111 => 3

[[],[],[[],[]],[],[],[]] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => 1011111 => 5

[[],[],[[[]]],[],[],[]] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [3,4,8,7,6,5,2,1] => 0011111 => 5

[[],[],[[],[]],[],[[]]] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [4,3,7,8,6,5,2,1] => 1001111 => 4

[[],[],[[],[]],[[[]]]] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => 1000111 => 3

[[],[],[[[]]],[[[]]]] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => 0000111 => 3

[[],[],[[],[],[]],[],[]] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [5,4,3,8,7,6,2,1] => 1101111 => 4

[[],[],[[[[]]]],[],[]] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [3,4,5,8,7,6,2,1] => 0001111 => 4

[[],[],[[],[],[]],[[]]] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [5,4,3,7,8,6,2,1] => 1100111 => 3

[[],[],[[[]],[]],[[]]] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [3,5,4,7,8,6,2,1] => 0100111 => 3

[[],[],[[[[]]]],[[]]] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [3,4,5,7,8,6,2,1] => 0000111 => 3

[[],[],[[],[],[],[]],[]] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [6,5,4,3,8,7,2,1] => 1110111 => 3

[[],[],[[],[],[[]]],[]] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [5,6,4,3,8,7,2,1] => 0110111 => 3

[[],[],[[],[[[]]]],[]] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [4,5,6,3,8,7,2,1] => 0010111 => 3

[[],[],[[[],[]],[]],[]] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 1010111 => 3

[[],[],[[[],[],[]]],[]] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [5,4,3,6,8,7,2,1] => 1100111 => 3

[[],[],[[[],[[]]]],[]] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [4,5,3,6,8,7,2,1] => 0100111 => 3

[[],[],[[[[[]]]]],[]] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [3,4,5,6,8,7,2,1] => 0000111 => 3

[[],[],[[],[],[],[],[]]] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => 1111011 => 4

[[],[],[[],[],[],[[]]]] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => 0111011 => 3

[[],[],[[],[],[[]],[]]] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [5,7,6,4,3,8,2,1] => 0111011 => 3

[[],[],[[],[],[[],[]]]] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [6,5,7,4,3,8,2,1] => 1011011 => 2

[[],[],[[],[],[[[]]]]] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => 0011011 => 2

[[],[],[[],[[]],[],[]]] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [4,7,6,5,3,8,2,1] => 0111011 => 3

[[],[],[[],[[],[]],[]]] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [5,4,7,6,3,8,2,1] => 1011011 => 2

[[],[],[[],[[],[],[]]]] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => 1101011 => 2

[[],[],[[],[[[],[]]]]] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => 1001011 => 2

[[],[],[[],[[[[]]]]]] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => 0001011 => 2

[[],[],[[[]],[],[],[]]] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [3,7,6,5,4,8,2,1] => 0111011 => 3

[[],[],[[[]],[[]],[]]] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [3,5,7,6,4,8,2,1] => 0011011 => 2

[[],[],[[[]],[[[]]]]] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [3,5,6,7,4,8,2,1] => 0001011 => 2

[[],[],[[[],[]],[],[]]] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [4,3,7,6,5,8,2,1] => 1011011 => 2

[[],[],[[[[]]],[],[]]] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1] => 0011011 => 2

[[],[],[[[[]]],[[]]]] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [3,4,6,7,5,8,2,1] => 0001011 => 2

[[],[],[[[],[[]]],[]]] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [4,5,3,7,6,8,2,1] => 0101011 => 2

[[],[],[[[[]],[]],[]]] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [3,5,4,7,6,8,2,1] => 0101011 => 2

[[],[],[[[[],[]]],[]]] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => 1001011 => 2

[[],[],[[[[[]]]],[]]] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [3,4,5,7,6,8,2,1] => 0001011 => 2

[[],[],[[[],[],[],[]]]] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => 1110011 => 3

[[],[],[[[],[[[]]]]]] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1] => 0010011 => 2

[[],[],[[[[]],[],[]]]] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [3,6,5,4,7,8,2,1] => 0110011 => 2

[[],[],[[[[]],[[]]]]] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [3,5,6,4,7,8,2,1] => 0010011 => 2

[[],[],[[[[],[]],[]]]] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [4,3,6,5,7,8,2,1] => 1010011 => 2

[[],[],[[[[[]]],[]]]] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [3,4,6,5,7,8,2,1] => 0010011 => 2

[[],[],[[[[],[],[]]]]] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => 1100011 => 2

[[],[],[[[[[]],[]]]]] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [3,5,4,6,7,8,2,1] => 0100011 => 2

[[],[],[[[[[],[]]]]]] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => 1000011 => 2

[[],[],[[[[[[]]]]]]] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => 0000011 => 2

[[],[[]],[],[],[],[],[]] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => 0111111 => 6

[[],[[]],[],[],[],[[]]] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [2,7,8,6,5,4,3,1] => 0011111 => 5

[[],[[]],[],[],[[]],[]] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => 0011111 => 5

[[],[[]],[],[],[[],[]]] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [2,7,6,8,5,4,3,1] => 0101111 => 4

[[],[[]],[],[],[[[]]]] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [2,6,7,8,5,4,3,1] => 0001111 => 4

[[],[[]],[],[[]],[],[]] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [2,5,8,7,6,4,3,1] => 0011111 => 5

[[],[[]],[],[[],[[]]]] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [2,6,7,5,8,4,3,1] => 0010111 => 3

[[],[[]],[],[[[],[]]]] => [.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [2,6,5,7,8,4,3,1] => 0100111 => 3

[[],[[]],[],[[[[]]]]] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [2,5,6,7,8,4,3,1] => 0000111 => 3

[[],[[]],[[]],[],[],[]] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [2,4,8,7,6,5,3,1] => 0011111 => 5

[[],[[]],[[]],[],[[]]] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [2,4,7,8,6,5,3,1] => 0001111 => 4

[[],[[]],[[]],[[]],[]] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => 0001111 => 4

[[],[[]],[[]],[[[]]]] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [2,4,6,7,8,5,3,1] => 0000111 => 3

[[],[[]],[[],[]],[],[]] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [2,5,4,8,7,6,3,1] => 0101111 => 4

[[],[[]],[[],[]],[[]]] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => 0100111 => 3

[[],[[]],[[[]]],[[]]] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [2,4,5,7,8,6,3,1] => 0000111 => 3

[[],[[]],[[],[],[]],[]] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [2,6,5,4,8,7,3,1] => 0110111 => 3

[[],[[]],[[],[[]]],[]] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [2,5,6,4,8,7,3,1] => 0010111 => 3

[[],[[]],[[[]],[]],[]] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => 0010111 => 3

[[],[[]],[[[[]]]],[]] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [2,4,5,6,8,7,3,1] => 0000111 => 3

[[],[[]],[[],[],[],[]]] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [2,7,6,5,4,8,3,1] => 0111011 => 3

[[],[[]],[[],[],[[]]]] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [2,6,7,5,4,8,3,1] => 0011011 => 2

[[],[[]],[[],[[[]]]]] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [2,5,6,7,4,8,3,1] => 0001011 => 2

[[],[[]],[[[]],[],[]]] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [2,4,7,6,5,8,3,1] => 0011011 => 2

[[],[[]],[[[]],[[]]]] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [2,4,6,7,5,8,3,1] => 0001011 => 2

[[],[[]],[[[],[]],[]]] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [2,5,4,7,6,8,3,1] => 0101011 => 2

[[],[[]],[[[],[],[]]]] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [2,6,5,4,7,8,3,1] => 0110011 => 2

[[],[[]],[[[],[[]]]]] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [2,5,6,4,7,8,3,1] => 0010011 => 2

[[],[[]],[[[[]],[]]]] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [2,4,6,5,7,8,3,1] => 0010011 => 2

[[],[[]],[[[[],[]]]]] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [2,5,4,6,7,8,3,1] => 0100011 => 2

[[],[[]],[[[[[]]]]]] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [2,4,5,6,7,8,3,1] => 0000011 => 2

[[],[[],[]],[],[],[],[]] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => 1011111 => 5

[[],[[[]]],[],[],[],[]] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => 0011111 => 5

[[],[[],[]],[],[[]],[]] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [3,2,6,8,7,5,4,1] => 1001111 => 4

[[],[[[]]],[],[[[]]]] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [2,3,6,7,8,5,4,1] => 0000111 => 3

[[],[[],[]],[[]],[[]]] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [3,2,5,7,8,6,4,1] => 1000111 => 3

[[],[[[]]],[[]],[[]]] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [2,3,5,7,8,6,4,1] => 0000111 => 3

[[],[[],[]],[[],[]],[]] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [3,2,6,5,8,7,4,1] => 1010111 => 3

[[],[[[]]],[[],[]],[]] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [2,3,6,5,8,7,4,1] => 0010111 => 3

[[],[[[]]],[[[]]],[]] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 0000111 => 3

[[],[[],[]],[[[]],[]]] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => 1001011 => 2

[[],[[],[]],[[[[]]]]] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [3,2,5,6,7,8,4,1] => 1000011 => 2

[[],[[[]]],[[],[],[]]] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [2,3,7,6,5,8,4,1] => 0011011 => 2

[[],[[[]]],[[[]],[]]] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [2,3,5,7,6,8,4,1] => 0001011 => 2

[[],[[[]]],[[[[]]]]] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [2,3,5,6,7,8,4,1] => 0000011 => 2

[[],[[],[],[]],[],[],[]] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => 1101111 => 4

[[],[[],[[]]],[],[],[]] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => 0101111 => 4

[[],[[[]],[]],[],[],[]] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => 0101111 => 4

[[],[[[],[]]],[],[],[]] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => 1001111 => 4

[[],[[[[]]]],[],[],[]] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => 0001111 => 4

[[],[[],[],[]],[],[[]]] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [4,3,2,7,8,6,5,1] => 1100111 => 3

[[],[[],[[]]],[],[[]]] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [3,4,2,7,8,6,5,1] => 0100111 => 3

[[],[[[],[]]],[],[[]]] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [3,2,4,7,8,6,5,1] => 1000111 => 3

[[],[[[[]]]],[],[[]]] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [2,3,4,7,8,6,5,1] => 0000111 => 3

[[],[[[]],[]],[[]],[]] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => 0100111 => 3

[[],[[[[]]]],[[]],[]] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [2,3,4,6,8,7,5,1] => 0000111 => 3

[[],[[[]],[]],[[[]]]] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [2,4,3,6,7,8,5,1] => 0100011 => 2

[[],[[[[]]]],[[],[]]] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [2,3,4,7,6,8,5,1] => 0001011 => 2

[[],[[[[]]]],[[[]]]] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [2,3,4,6,7,8,5,1] => 0000011 => 2

[[],[[],[],[],[]],[],[]] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [5,4,3,2,8,7,6,1] => 1110111 => 3

[[],[[[]],[],[]],[],[]] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [2,5,4,3,8,7,6,1] => 0110111 => 3

[[],[[[]],[[]]],[],[]] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [2,4,5,3,8,7,6,1] => 0010111 => 3

[[],[[[[]]],[]],[],[]] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [2,3,5,4,8,7,6,1] => 0010111 => 3

[[],[[[],[],[]]],[],[]] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [4,3,2,5,8,7,6,1] => 1100111 => 3

[[],[[[],[[]]]],[],[]] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [3,4,2,5,8,7,6,1] => 0100111 => 3

[[],[[[[]],[]]],[],[]] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [2,4,3,5,8,7,6,1] => 0100111 => 3

[[],[[[[[]]]]],[],[]] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [2,3,4,5,8,7,6,1] => 0000111 => 3

[[],[[],[],[],[]],[[]]] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [5,4,3,2,7,8,6,1] => 1110011 => 3

[[],[[],[[]],[]],[[]]] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [3,5,4,2,7,8,6,1] => 0110011 => 2

[[],[[],[[[]]]],[[]]] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [3,4,5,2,7,8,6,1] => 0010011 => 2

[[],[[[]],[],[]],[[]]] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [2,5,4,3,7,8,6,1] => 0110011 => 2

[[],[[[]],[[]]],[[]]] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [2,4,5,3,7,8,6,1] => 0010011 => 2

[[],[[[],[]],[]],[[]]] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [3,2,5,4,7,8,6,1] => 1010011 => 2

[[],[[[[]]],[]],[[]]] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [2,3,5,4,7,8,6,1] => 0010011 => 2

[[],[[[],[],[]]],[[]]] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [4,3,2,5,7,8,6,1] => 1100011 => 2

[[],[[[],[[]]]],[[]]] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [3,4,2,5,7,8,6,1] => 0100011 => 2

[[],[[[[],[]]]],[[]]] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [3,2,4,5,7,8,6,1] => 1000011 => 2

[[],[[[[[]]]]],[[]]] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [2,3,4,5,7,8,6,1] => 0000011 => 2

[[],[[],[],[],[],[]],[]] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [6,5,4,3,2,8,7,1] => 1111011 => 4

[[],[[],[],[[]],[]],[]] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [4,6,5,3,2,8,7,1] => 0111011 => 3

[[],[[],[],[[],[]]],[]] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [5,4,6,3,2,8,7,1] => 1011011 => 2

[[],[[],[],[[[]]]],[]] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [4,5,6,3,2,8,7,1] => 0011011 => 2

[[],[[],[[]],[],[]],[]] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [3,6,5,4,2,8,7,1] => 0111011 => 3

[[],[[],[[]],[[]]],[]] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [3,5,6,4,2,8,7,1] => 0011011 => 2

[[],[[],[[],[]],[]],[]] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [4,3,6,5,2,8,7,1] => 1011011 => 2

[[],[[],[[],[],[]]],[]] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [5,4,3,6,2,8,7,1] => 1101011 => 2

[[],[[],[[],[[]]]],[]] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => 0101011 => 2

[[],[[],[[[]],[]]],[]] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [3,5,4,6,2,8,7,1] => 0101011 => 2

[[],[[],[[[[]]]]],[]] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [3,4,5,6,2,8,7,1] => 0001011 => 2

[[],[[[]],[],[],[]],[]] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [2,6,5,4,3,8,7,1] => 0111011 => 3

[[],[[[]],[[]],[]],[]] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [2,4,6,5,3,8,7,1] => 0011011 => 2

[[],[[[]],[[[]]]],[]] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [2,4,5,6,3,8,7,1] => 0001011 => 2

[[],[[[],[]],[],[]],[]] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 1011011 => 2

[[],[[[[]]],[[]]],[]] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [2,3,5,6,4,8,7,1] => 0001011 => 2

[[],[[[],[],[]],[]],[]] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [4,3,2,6,5,8,7,1] => 1101011 => 2

[[],[[[[]],[]],[]],[]] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => 0101011 => 2

[[],[[[[],[]]],[]],[]] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [3,2,4,6,5,8,7,1] => 1001011 => 2

[[],[[[[[]]]],[]],[]] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [2,3,4,6,5,8,7,1] => 0001011 => 2

[[],[[[],[],[],[]]],[]] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [5,4,3,2,6,8,7,1] => 1110011 => 3

[[],[[[],[],[[]]]],[]] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [4,5,3,2,6,8,7,1] => 0110011 => 2

[[],[[[[]],[],[]]],[]] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [2,5,4,3,6,8,7,1] => 0110011 => 2

[[],[[[[]],[[]]]],[]] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [2,4,5,3,6,8,7,1] => 0010011 => 2

[[],[[[[],[]],[]]],[]] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [3,2,5,4,6,8,7,1] => 1010011 => 2

[[],[[[[],[],[]]]],[]] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [4,3,2,5,6,8,7,1] => 1100011 => 2

[[],[[[[],[[]]]]],[]] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [3,4,2,5,6,8,7,1] => 0100011 => 2

[[],[[[[[]],[]]]],[]] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [2,4,3,5,6,8,7,1] => 0100011 => 2

[[],[[[[[],[]]]]],[]] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [3,2,4,5,6,8,7,1] => 1000011 => 2

[[],[[[[[[]]]]]],[]] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [2,3,4,5,6,8,7,1] => 0000011 => 2

[[],[[],[],[],[],[],[]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 1111101 => 5

[[],[[],[],[],[],[[]]]] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => 0111101 => 4

[[],[[],[],[],[[]],[]]] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [5,7,6,4,3,2,8,1] => 0111101 => 4

[[],[[],[],[],[[],[]]]] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 1011101 => 3

[[],[[],[],[],[[[]]]]] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => 0011101 => 3

[[],[[],[],[[]],[],[]]] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [4,7,6,5,3,2,8,1] => 0111101 => 4

[[],[[],[],[[]],[[]]]] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [4,6,7,5,3,2,8,1] => 0011101 => 3

[[],[[],[],[[],[],[]]]] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1] => 1101101 => 2

[[],[[],[],[[[]],[]]]] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => 0101101 => 2

[[],[[],[],[[[[]]]]]] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => 0001101 => 2

[[],[[],[[]],[[]],[]]] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [3,5,7,6,4,2,8,1] => 0011101 => 3

[[],[[],[[]],[[[]]]]] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [3,5,6,7,4,2,8,1] => 0001101 => 2

[[],[[],[[],[]],[],[]]] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [4,3,7,6,5,2,8,1] => 1011101 => 3

[[],[[],[[[]]],[],[]]] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [3,4,7,6,5,2,8,1] => 0011101 => 3

[[],[[],[[],[]],[[]]]] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [4,3,6,7,5,2,8,1] => 1001101 => 2

[[],[[],[[[]]],[[]]]] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [3,4,6,7,5,2,8,1] => 0001101 => 2

[[],[[],[[],[],[]],[]]] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [5,4,3,7,6,2,8,1] => 1101101 => 2

[[],[[],[[],[[]]],[]]] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [4,5,3,7,6,2,8,1] => 0101101 => 2

[[],[[],[[[]],[]],[]]] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [3,5,4,7,6,2,8,1] => 0101101 => 2

[[],[[],[[[[]]]],[]]] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [3,4,5,7,6,2,8,1] => 0001101 => 2

[[],[[],[[],[],[],[]]]] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 1110101 => 3

[[],[[],[[],[[]],[]]]] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [4,6,5,3,7,2,8,1] => 0110101 => 2

[[],[[],[[],[[],[]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 1010101 => 1

[[],[[],[[],[[[]]]]]] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => 0010101 => 1

[[],[[],[[[]],[],[]]]] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [3,6,5,4,7,2,8,1] => 0110101 => 2

[[],[[],[[[]],[[]]]]] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => 0010101 => 1

[[],[[],[[[],[]],[]]]] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => 1010101 => 1

[[],[[],[[[[]]],[]]]] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [3,4,6,5,7,2,8,1] => 0010101 => 1

[[],[[],[[[],[],[]]]]] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => 1100101 => 2

[[],[[],[[[],[[]]]]]] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => 0100101 => 1

[[],[[],[[[[]],[]]]]] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [3,5,4,6,7,2,8,1] => 0100101 => 1

[[],[[],[[[[],[]]]]]] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [4,3,5,6,7,2,8,1] => 1000101 => 1

[[],[[],[[[[[]]]]]]] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => 0000101 => 1

[[],[[[]],[],[],[],[]]] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1] => 0111101 => 4

[[],[[[]],[],[[],[]]]] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [2,6,5,7,4,3,8,1] => 0101101 => 2

[[],[[[]],[],[[[]]]]] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [2,5,6,7,4,3,8,1] => 0001101 => 2

[[],[[[]],[[]],[[]]]] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [2,4,6,7,5,3,8,1] => 0001101 => 2

[[],[[[]],[[],[]],[]]] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [2,5,4,7,6,3,8,1] => 0101101 => 2

[[],[[[]],[[[]],[]]]] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => 0010101 => 1

[[],[[[]],[[[],[]]]]] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [2,5,4,6,7,3,8,1] => 0100101 => 1

[[],[[[]],[[[[]]]]]] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [2,4,5,6,7,3,8,1] => 0000101 => 1

[[],[[[],[]],[],[],[]]] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [3,2,7,6,5,4,8,1] => 1011101 => 3

[[],[[[[]]],[],[],[]]] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1] => 0011101 => 3

[[],[[[],[]],[],[[]]]] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [3,2,6,7,5,4,8,1] => 1001101 => 2

[[],[[[],[]],[[]],[]]] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [3,2,5,7,6,4,8,1] => 1001101 => 2

[[],[[[[]]],[[]],[]]] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [2,3,5,7,6,4,8,1] => 0001101 => 2

[[],[[[],[]],[[],[]]]] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => 1010101 => 1

[[],[[[],[]],[[[]]]]] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [3,2,5,6,7,4,8,1] => 1000101 => 1

[[],[[[[]]],[[[]]]]] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [2,3,5,6,7,4,8,1] => 0000101 => 1

[[],[[[],[],[]],[],[]]] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => 1101101 => 2

[[],[[[],[[]]],[],[]]] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [3,4,2,7,6,5,8,1] => 0101101 => 2

[[],[[[[]],[]],[],[]]] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [2,4,3,7,6,5,8,1] => 0101101 => 2

[[],[[[[],[]]],[],[]]] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1] => 1001101 => 2

[[],[[[[[]]]],[],[]]] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1] => 0001101 => 2

[[],[[[],[],[]],[[]]]] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [4,3,2,6,7,5,8,1] => 1100101 => 2

[[],[[[],[[]]],[[]]]] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => 0100101 => 1

[[],[[[[]],[]],[[]]]] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [2,4,3,6,7,5,8,1] => 0100101 => 1

[[],[[[[[]]]],[[]]]] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [2,3,4,6,7,5,8,1] => 0000101 => 1

[[],[[[],[],[],[]],[]]] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1] => 1110101 => 3

[[],[[[],[[]],[]],[]]] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [3,5,4,2,7,6,8,1] => 0110101 => 2

[[],[[[],[[],[]]],[]]] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 1010101 => 1

[[],[[[],[[[]]]],[]]] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [3,4,5,2,7,6,8,1] => 0010101 => 1

[[],[[[[]],[],[]],[]]] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [2,5,4,3,7,6,8,1] => 0110101 => 2

[[],[[[[],[]],[]],[]]] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 1010101 => 1

[[],[[[[[]]],[]],[]]] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [2,3,5,4,7,6,8,1] => 0010101 => 1

[[],[[[[],[],[]]],[]]] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1] => 1100101 => 2

[[],[[[[],[[]]]],[]]] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [3,4,2,5,7,6,8,1] => 0100101 => 1

[[],[[[[[]],[]]],[]]] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1] => 0100101 => 1

[[],[[[[[],[]]]],[]]] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => 1000101 => 1

[[],[[[[[[]]]]],[]]] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1] => 0000101 => 1

[[],[[[],[],[],[],[]]]] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => 1111001 => 4

[[],[[[],[],[[],[]]]]] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => 1011001 => 2

[[],[[[],[],[[[]]]]]] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => 0011001 => 2

[[],[[[],[[]],[],[]]]] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [3,6,5,4,2,7,8,1] => 0111001 => 3

[[],[[[],[[]],[[]]]]] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [3,5,6,4,2,7,8,1] => 0011001 => 2

[[],[[[],[[[]]],[]]]] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [3,4,6,5,2,7,8,1] => 0011001 => 2

[[],[[[],[[],[],[]]]]] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => 1101001 => 2

[[],[[[],[[[]],[]]]]] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [3,5,4,6,2,7,8,1] => 0101001 => 1

[[],[[[],[[[],[]]]]]] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => 1001001 => 1

[[],[[[],[[[[]]]]]]] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => 0001001 => 1

[[],[[[[]],[],[],[]]]] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [2,6,5,4,3,7,8,1] => 0111001 => 3

[[],[[[[]],[],[[]]]]] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [2,5,6,4,3,7,8,1] => 0011001 => 2

[[],[[[[]],[[]],[]]]] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [2,4,6,5,3,7,8,1] => 0011001 => 2

[[],[[[[]],[[],[]]]]] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [2,5,4,6,3,7,8,1] => 0101001 => 1

[[],[[[[]],[[[]]]]]] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => [2,4,5,6,3,7,8,1] => 0001001 => 1

[[],[[[[[]]],[],[]]]] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [2,3,6,5,4,7,8,1] => 0011001 => 2

[[],[[[[],[]],[[]]]]] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [3,2,5,6,4,7,8,1] => 1001001 => 1

[[],[[[[[]]],[[]]]]] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => [2,3,5,6,4,7,8,1] => 0001001 => 1

[[],[[[[],[],[]],[]]]] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [4,3,2,6,5,7,8,1] => 1101001 => 2

[[],[[[[],[[]]],[]]]] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [3,4,2,6,5,7,8,1] => 0101001 => 1

[[],[[[[[]],[]],[]]]] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => 0101001 => 1

[[],[[[[[[]]]],[]]]] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [2,3,4,6,5,7,8,1] => 0001001 => 1

[[],[[[[],[],[],[]]]]] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => 1110001 => 3

[[],[[[[],[],[[]]]]]] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => 0110001 => 2

[[],[[[[],[[]],[]]]]] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [3,5,4,2,6,7,8,1] => 0110001 => 2

[[],[[[[],[[],[]]]]]] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => 1010001 => 1

[[],[[[[],[[[]]]]]]] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 0010001 => 1

[[],[[[[[]],[],[]]]]] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1] => 0110001 => 2

[[],[[[[[]],[[]]]]]] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => [2,4,5,3,6,7,8,1] => 0010001 => 1

[[],[[[[[],[]],[]]]]] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [3,2,5,4,6,7,8,1] => 1010001 => 1

[[],[[[[[[]]],[]]]]] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1] => 0010001 => 1

[[],[[[[[],[],[]]]]]] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 1100001 => 2

[[],[[[[[],[[]]]]]]] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 0100001 => 1

[[],[[[[[[]],[]]]]]] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [2,4,3,5,6,7,8,1] => 0100001 => 1

[[],[[[[[[],[]]]]]]] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 1000001 => 1

[[],[[[[[[[]]]]]]]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 0000001 => 1

[[[]],[],[],[],[],[],[]] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 0111111 => 6

[[[]],[],[],[],[],[[]]] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 0011111 => 5

[[[]],[],[],[],[[]],[]] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => 0011111 => 5

[[[]],[],[],[],[[],[]]] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => 0101111 => 4

[[[]],[],[],[],[[[]]]] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 0001111 => 4

[[[]],[],[],[[]],[],[]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => 0011111 => 5

[[[]],[],[],[[],[]],[]] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => 0101111 => 4

[[[]],[],[],[[],[],[]]] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => 0110111 => 3

[[[]],[],[],[[],[[]]]] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => 0010111 => 3

[[[]],[],[],[[[]],[]]] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,5,7,6,8,4,3,2] => 0010111 => 3

[[[]],[],[],[[[],[]]]] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,6,5,7,8,4,3,2] => 0100111 => 3

[[[]],[],[],[[[[]]]]] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,5,6,7,8,4,3,2] => 0000111 => 3

[[[]],[],[[]],[],[],[]] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,4,8,7,6,5,3,2] => 0011111 => 5

[[[]],[],[[]],[],[[]]] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,4,7,8,6,5,3,2] => 0001111 => 4

[[[]],[],[[]],[[]],[]] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,4,6,8,7,5,3,2] => 0001111 => 4

[[[]],[],[[]],[[[]]]] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,4,6,7,8,5,3,2] => 0000111 => 3

[[[]],[],[[[]]],[],[]] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,4,5,8,7,6,3,2] => 0001111 => 4

[[[]],[],[[],[]],[[]]] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,5,4,7,8,6,3,2] => 0100111 => 3

[[[]],[],[[[]]],[[]]] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,4,5,7,8,6,3,2] => 0000111 => 3

[[[]],[],[[],[],[]],[]] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,6,5,4,8,7,3,2] => 0110111 => 3

[[[]],[],[[[]],[]],[]] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,4,6,5,8,7,3,2] => 0010111 => 3

[[[]],[],[[],[],[],[]]] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => 0111011 => 3

[[[]],[],[[[]],[],[]]] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,4,7,6,5,8,3,2] => 0011011 => 2

[[[]],[],[[[]],[[]]]] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,4,6,7,5,8,3,2] => 0001011 => 2

[[[]],[],[[[],[],[]]]] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,6,5,4,7,8,3,2] => 0110011 => 2

[[[]],[],[[[],[[]]]]] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,5,6,4,7,8,3,2] => 0010011 => 2

[[[]],[],[[[[],[]]]]] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => 0100011 => 2

[[[]],[],[[[[[]]]]]] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => 0000011 => 2

[[[]],[[]],[],[],[],[]] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => 0011111 => 5

[[[]],[[]],[],[],[[]]] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,3,7,8,6,5,4,2] => 0001111 => 4

[[[]],[[]],[],[[]],[]] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,3,6,8,7,5,4,2] => 0001111 => 4

[[[]],[[]],[],[[[]]]] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,3,6,7,8,5,4,2] => 0000111 => 3

[[[]],[[]],[[]],[],[]] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,3,5,8,7,6,4,2] => 0001111 => 4

[[[]],[[]],[[]],[[]]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => 0000111 => 3

[[[]],[[]],[[[]]],[]] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,3,5,6,8,7,4,2] => 0000111 => 3

[[[]],[[]],[[],[[]]]] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,3,6,7,5,8,4,2] => 0001011 => 2

[[[]],[[]],[[[]],[]]] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,3,5,7,6,8,4,2] => 0001011 => 2

[[[]],[[]],[[[],[]]]] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,3,6,5,7,8,4,2] => 0010011 => 2

[[[]],[[]],[[[[]]]]] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,3,5,6,7,8,4,2] => 0000011 => 2

[[[]],[[],[]],[],[],[]] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => 0101111 => 4

[[[]],[[[]]],[],[],[]] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => 0001111 => 4

[[[]],[[],[]],[],[[]]] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => 0100111 => 3

[[[]],[[],[]],[[]],[]] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,4,3,6,8,7,5,2] => 0100111 => 3

[[[]],[[],[]],[[],[]]] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,4,3,7,6,8,5,2] => 0101011 => 2

[[[]],[[],[]],[[[]]]] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,4,3,6,7,8,5,2] => 0100011 => 2

[[[]],[[[]]],[[],[]]] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,3,4,7,6,8,5,2] => 0001011 => 2

[[[]],[[[]]],[[[]]]] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,3,4,6,7,8,5,2] => 0000011 => 2

[[[]],[[],[],[]],[],[]] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,5,4,3,8,7,6,2] => 0110111 => 3

[[[]],[[],[[]]],[],[]] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,4,5,3,8,7,6,2] => 0010111 => 3

[[[]],[[[]],[]],[],[]] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,3,5,4,8,7,6,2] => 0010111 => 3

[[[]],[[[],[]]],[],[]] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,4,3,5,8,7,6,2] => 0100111 => 3

[[[]],[[[[]]]],[],[]] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,3,4,5,8,7,6,2] => 0000111 => 3

[[[]],[[],[[]]],[[]]] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,4,5,3,7,8,6,2] => 0010011 => 2

[[[]],[[[]],[]],[[]]] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => 0010011 => 2

[[[]],[[[],[]]],[[]]] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,4,3,5,7,8,6,2] => 0100011 => 2

[[[]],[[[[]]]],[[]]] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,3,4,5,7,8,6,2] => 0000011 => 2

[[[]],[[],[],[],[]],[]] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => 0111011 => 3

[[[]],[[],[],[[]]],[]] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => 0011011 => 2

[[[]],[[],[[]],[]],[]] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,4,6,5,3,8,7,2] => 0011011 => 2

[[[]],[[],[[[]]]],[]] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,4,5,6,3,8,7,2] => 0001011 => 2

[[[]],[[[]],[],[]],[]] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,3,6,5,4,8,7,2] => 0011011 => 2

[[[]],[[[],[]],[]],[]] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => 0101011 => 2

[[[]],[[[],[],[]]],[]] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,5,4,3,6,8,7,2] => 0110011 => 2

[[[]],[[[],[[]]]],[]] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => 0010011 => 2

[[[]],[[[[[]]]]],[]] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => 0000011 => 2

[[[]],[[],[],[],[],[]]] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,7,6,5,4,3,8,2] => 0111101 => 4

[[[]],[[],[],[],[[]]]] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,6,7,5,4,3,8,2] => 0011101 => 3

[[[]],[[],[],[[],[]]]] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => 0101101 => 2

[[[]],[[],[[]],[[]]]] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => 0001101 => 2

[[[]],[[],[[],[[]]]]] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => 0010101 => 1

[[[]],[[],[[[]],[]]]] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,4,6,5,7,3,8,2] => 0010101 => 1

[[[]],[[],[[[],[]]]]] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => 0100101 => 1

[[[]],[[],[[[[]]]]]] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => 0000101 => 1

[[[]],[[[]],[[]],[]]] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,3,5,7,6,4,8,2] => 0001101 => 2

[[[]],[[[]],[[],[]]]] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,3,6,5,7,4,8,2] => 0010101 => 1

[[[]],[[[]],[[[]]]]] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,3,5,6,7,4,8,2] => 0000101 => 1

[[[]],[[[[]]],[],[]]] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,3,4,7,6,5,8,2] => 0001101 => 2

[[[]],[[[],[]],[[]]]] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,4,3,6,7,5,8,2] => 0100101 => 1

[[[]],[[[[]]],[[]]]] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,3,4,6,7,5,8,2] => 0000101 => 1

[[[]],[[[[]],[]],[]]] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,3,5,4,7,6,8,2] => 0010101 => 1

[[[]],[[[[[]]]],[]]] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,3,4,5,7,6,8,2] => 0000101 => 1

[[[]],[[[],[],[],[]]]] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,6,5,4,3,7,8,2] => 0111001 => 3

[[[]],[[[],[[],[]]]]] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,5,4,6,3,7,8,2] => 0101001 => 1

[[[]],[[[[]],[[]]]]] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,3,5,6,4,7,8,2] => 0001001 => 1

[[[]],[[[[],[]],[]]]] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,4,3,6,5,7,8,2] => 0101001 => 1

[[[]],[[[[[]]],[]]]] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,3,4,6,5,7,8,2] => 0001001 => 1

[[[]],[[[[],[],[]]]]] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,5,4,3,6,7,8,2] => 0110001 => 2

[[[]],[[[[],[[]]]]]] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => 0010001 => 1

[[[]],[[[[[]],[]]]]] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,3,5,4,6,7,8,2] => 0010001 => 1

[[[]],[[[[[],[]]]]]] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => 0100001 => 1

[[[]],[[[[[[]]]]]]] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,3,4,5,6,7,8,2] => 0000001 => 1

[[[],[]],[],[],[],[],[]] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 1011111 => 5

[[[[]]],[],[],[],[],[]] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => 0011111 => 5

[[[],[]],[],[],[],[[]]] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [2,1,7,8,6,5,4,3] => 1001111 => 4

[[[[]]],[],[],[],[[]]] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,2,7,8,6,5,4,3] => 0001111 => 4

[[[],[]],[],[],[[]],[]] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [2,1,6,8,7,5,4,3] => 1001111 => 4

[[[],[]],[],[],[[],[]]] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => 1010111 => 3

[[[],[]],[],[],[[[]]]] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => 1000111 => 3

[[[[]]],[],[],[[],[]]] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,2,7,6,8,5,4,3] => 0010111 => 3

[[[[]]],[],[],[[[]]]] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 0000111 => 3

[[[],[]],[],[[]],[],[]] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [2,1,5,8,7,6,4,3] => 1001111 => 4

[[[[]]],[],[[]],[],[]] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,2,5,8,7,6,4,3] => 0001111 => 4

[[[],[]],[],[[]],[[]]] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => 1000111 => 3

[[[],[]],[],[[],[]],[]] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [2,1,6,5,8,7,4,3] => 1010111 => 3

[[[],[]],[],[[[]]],[]] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [2,1,5,6,8,7,4,3] => 1000111 => 3

[[[[]]],[],[[],[]],[]] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,2,6,5,8,7,4,3] => 0010111 => 3

[[[[]]],[],[[[]]],[]] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,2,5,6,8,7,4,3] => 0000111 => 3

[[[],[]],[],[[],[],[]]] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [2,1,7,6,5,8,4,3] => 1011011 => 2

[[[],[]],[],[[],[[]]]] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => 1001011 => 2

[[[],[]],[],[[[]],[]]] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [2,1,5,7,6,8,4,3] => 1001011 => 2

[[[],[]],[],[[[],[]]]] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [2,1,6,5,7,8,4,3] => 1010011 => 2

[[[],[]],[],[[[[]]]]] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [2,1,5,6,7,8,4,3] => 1000011 => 2

[[[[]]],[],[[],[],[]]] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,2,7,6,5,8,4,3] => 0011011 => 2

[[[[]]],[],[[[]],[]]] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,2,5,7,6,8,4,3] => 0001011 => 2

[[[[]]],[],[[[],[]]]] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,2,6,5,7,8,4,3] => 0010011 => 2

[[[[]]],[],[[[[]]]]] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,2,5,6,7,8,4,3] => 0000011 => 2

[[[],[]],[[]],[],[],[]] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => 1001111 => 4

[[[[]]],[[]],[],[],[]] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => 0001111 => 4

[[[],[]],[[]],[],[[]]] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [2,1,4,7,8,6,5,3] => 1000111 => 3

[[[[]]],[[]],[],[[]]] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,2,4,7,8,6,5,3] => 0000111 => 3

[[[],[]],[[]],[[]],[]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => 1000111 => 3

[[[[]]],[[]],[[]],[]] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,2,4,6,8,7,5,3] => 0000111 => 3

[[[],[]],[[]],[[],[]]] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [2,1,4,7,6,8,5,3] => 1001011 => 2

[[[],[]],[[]],[[[]]]] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [2,1,4,6,7,8,5,3] => 1000011 => 2

[[[[]]],[[]],[[],[]]] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,2,4,7,6,8,5,3] => 0001011 => 2

[[[[]]],[[]],[[[]]]] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,2,4,6,7,8,5,3] => 0000011 => 2

[[[],[]],[[],[]],[],[]] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [2,1,5,4,8,7,6,3] => 1010111 => 3

[[[],[]],[[[]]],[],[]] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => 1000111 => 3

[[[[]]],[[],[]],[],[]] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => 0010111 => 3

[[[[]]],[[[]]],[],[]] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => 0000111 => 3

[[[],[]],[[],[]],[[]]] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [2,1,5,4,7,8,6,3] => 1010011 => 2

[[[],[]],[[[]]],[[]]] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [2,1,4,5,7,8,6,3] => 1000011 => 2

[[[[]]],[[[]]],[[]]] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,2,4,5,7,8,6,3] => 0000011 => 2

[[[],[]],[[],[],[]],[]] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [2,1,6,5,4,8,7,3] => 1011011 => 2

[[[],[]],[[],[[]]],[]] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [2,1,5,6,4,8,7,3] => 1001011 => 2

[[[],[]],[[[]],[]],[]] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => 1001011 => 2

[[[],[]],[[[],[]]],[]] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [2,1,5,4,6,8,7,3] => 1010011 => 2

[[[],[]],[[[[]]]],[]] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [2,1,4,5,6,8,7,3] => 1000011 => 2

[[[[]]],[[],[],[]],[]] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,2,6,5,4,8,7,3] => 0011011 => 2

[[[[]]],[[[],[]]],[]] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,2,5,4,6,8,7,3] => 0010011 => 2

[[[[]]],[[[[]]]],[]] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,2,4,5,6,8,7,3] => 0000011 => 2

[[[],[]],[[],[],[],[]]] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [2,1,7,6,5,4,8,3] => 1011101 => 3

[[[],[]],[[],[],[[]]]] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [2,1,6,7,5,4,8,3] => 1001101 => 2

[[[],[]],[[],[[]],[]]] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [2,1,5,7,6,4,8,3] => 1001101 => 2

[[[],[]],[[],[[],[]]]] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => 1010101 => 1

[[[],[]],[[],[[[]]]]] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [2,1,5,6,7,4,8,3] => 1000101 => 1

[[[],[]],[[[]],[],[]]] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [2,1,4,7,6,5,8,3] => 1001101 => 2

[[[],[]],[[[]],[[]]]] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [2,1,4,6,7,5,8,3] => 1000101 => 1

[[[],[]],[[[],[]],[]]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => 1010101 => 1

[[[],[]],[[[],[[]]]]] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [2,1,5,6,4,7,8,3] => 1001001 => 1

[[[],[]],[[[[],[]]]]] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [2,1,5,4,6,7,8,3] => 1010001 => 1

[[[],[]],[[[[[]]]]]] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [2,1,4,5,6,7,8,3] => 1000001 => 1

[[[[]]],[[],[],[],[]]] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,2,7,6,5,4,8,3] => 0011101 => 3

[[[[]]],[[],[[]],[]]] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,2,5,7,6,4,8,3] => 0001101 => 2

[[[[]]],[[],[[[]]]]] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,2,5,6,7,4,8,3] => 0000101 => 1

[[[[]]],[[[]],[],[]]] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,2,4,7,6,5,8,3] => 0001101 => 2

[[[[]]],[[[],[]],[]]] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,2,5,4,7,6,8,3] => 0010101 => 1

[[[[]]],[[[],[],[]]]] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,2,6,5,4,7,8,3] => 0011001 => 2

[[[[]]],[[[],[[]]]]] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,2,5,6,4,7,8,3] => 0001001 => 1

[[[[]]],[[[[]],[]]]] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,2,4,6,5,7,8,3] => 0001001 => 1

[[[[]]],[[[[],[]]]]] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => 0010001 => 1

[[[[]]],[[[[[]]]]]] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,2,4,5,6,7,8,3] => 0000001 => 1

[[[],[],[]],[],[],[],[]] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 1101111 => 4

[[[],[[]]],[],[],[],[]] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => 0101111 => 4

[[[[]],[]],[],[],[],[]] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => 0101111 => 4

[[[[],[]]],[],[],[],[]] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => 1001111 => 4

[[[[[]]]],[],[],[],[]] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => 0001111 => 4

[[[],[],[]],[],[],[[]]] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => 1100111 => 3

[[[],[[]]],[],[],[[]]] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [2,3,1,7,8,6,5,4] => 0100111 => 3

[[[[],[]]],[],[],[[]]] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [2,1,3,7,8,6,5,4] => 1000111 => 3

[[[[[]]]],[],[],[[]]] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => 0000111 => 3

[[[],[],[]],[],[[]],[]] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => 1100111 => 3

[[[],[[]]],[],[[]],[]] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [2,3,1,6,8,7,5,4] => 0100111 => 3

[[[[]],[]],[],[[]],[]] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => 0100111 => 3

[[[[],[]]],[],[[]],[]] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [2,1,3,6,8,7,5,4] => 1000111 => 3

[[[[[]]]],[],[[]],[]] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => 0000111 => 3

[[[],[],[]],[],[[],[]]] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => 1101011 => 2

[[[],[],[]],[],[[[]]]] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => 1100011 => 2

[[[],[[]]],[],[[],[]]] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => 0101011 => 2

[[[],[[]]],[],[[[]]]] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [2,3,1,6,7,8,5,4] => 0100011 => 2

[[[[]],[]],[],[[],[]]] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,3,2,7,6,8,5,4] => 0101011 => 2

[[[[]],[]],[],[[[]]]] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => 0100011 => 2

[[[[],[]]],[],[[[]]]] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [2,1,3,6,7,8,5,4] => 1000011 => 2

[[[[[]]]],[],[[],[]]] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => 0001011 => 2

[[[[[]]]],[],[[[]]]] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => 0000011 => 2

[[[],[],[]],[[]],[],[]] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => 1100111 => 3

[[[[]],[]],[[]],[],[]] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,3,2,5,8,7,6,4] => 0100111 => 3

[[[[[]]]],[[]],[],[]] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => 0000111 => 3

[[[],[],[]],[[]],[[]]] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => 1100011 => 2

[[[],[[]]],[[]],[[]]] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [2,3,1,5,7,8,6,4] => 0100011 => 2

[[[[]],[]],[[]],[[]]] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,3,2,5,7,8,6,4] => 0100011 => 2

[[[[[]]]],[[]],[[]]] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => 0000011 => 2

[[[],[],[]],[[],[]],[]] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => 1101011 => 2

[[[],[],[]],[[[]]],[]] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => 1100011 => 2

[[[],[[]]],[[],[]],[]] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => 0101011 => 2

[[[[]],[]],[[],[]],[]] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => 0101011 => 2

[[[[]],[]],[[[]]],[]] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,3,2,5,6,8,7,4] => 0100011 => 2

[[[[],[]]],[[],[]],[]] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => 1001011 => 2

[[[[[]]]],[[],[]],[]] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => 0001011 => 2

[[[[[]]]],[[[]]],[]] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => 0000011 => 2

[[[],[],[]],[[],[],[]]] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => 1101101 => 2

[[[],[],[]],[[],[[]]]] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => 1100101 => 2

[[[],[],[]],[[[]],[]]] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => 1100101 => 2

[[[],[],[]],[[[],[]]]] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => 1101001 => 2

[[[],[],[]],[[[[]]]]] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => 1100001 => 2

[[[],[[]]],[[],[],[]]] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [2,3,1,7,6,5,8,4] => 0101101 => 2

[[[],[[]]],[[],[[]]]] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => 0100101 => 1

[[[],[[]]],[[[]],[]]] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [2,3,1,5,7,6,8,4] => 0100101 => 1

[[[],[[]]],[[[[]]]]] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => 0100001 => 1

[[[[]],[]],[[],[],[]]] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,3,2,7,6,5,8,4] => 0101101 => 2

[[[[]],[]],[[],[[]]]] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => 0100101 => 1

[[[[]],[]],[[[]],[]]] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,3,2,5,7,6,8,4] => 0100101 => 1

[[[[]],[]],[[[],[]]]] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => 0101001 => 1

[[[[]],[]],[[[[]]]]] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,3,2,5,6,7,8,4] => 0100001 => 1

[[[[],[]]],[[[]],[]]] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => 1000101 => 1

[[[[],[]]],[[[[]]]]] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [2,1,3,5,6,7,8,4] => 1000001 => 1

[[[[[]]]],[[],[],[]]] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => 0001101 => 2

[[[[[]]]],[[],[[]]]] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => 0000101 => 1

[[[[[]]]],[[[]],[]]] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => 0000101 => 1

[[[[[]]]],[[[],[]]]] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => 0001001 => 1

[[[[[]]]],[[[[]]]]] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => 0000001 => 1

[[[],[],[],[]],[],[],[]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 1110111 => 3

[[[],[],[[]]],[],[],[]] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => 0110111 => 3

[[[],[[]],[]],[],[],[]] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => 0110111 => 3

[[[],[[],[]]],[],[],[]] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => 1010111 => 3

[[[],[[[]]]],[],[],[]] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => 0010111 => 3

[[[[]],[],[]],[],[],[]] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => 0110111 => 3

[[[[]],[[]]],[],[],[]] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => 0010111 => 3

[[[[],[]],[]],[],[],[]] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => 1010111 => 3

[[[[[]]],[]],[],[],[]] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => 0010111 => 3

[[[[],[],[]]],[],[],[]] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => 1100111 => 3

[[[[],[[]]]],[],[],[]] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => 0100111 => 3

[[[[[]],[]]],[],[],[]] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => 0100111 => 3

[[[[[],[]]]],[],[],[]] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => 1000111 => 3

[[[[[[]]]]],[],[],[]] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => 0000111 => 3

[[[],[],[],[]],[],[[]]] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => 1110011 => 3

[[[],[],[[]]],[],[[]]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 0110011 => 2

[[[],[[]],[]],[],[[]]] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => 0110011 => 2

[[[],[[],[]]],[],[[]]] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => 1010011 => 2

[[[],[[[]]]],[],[[]]] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [2,3,4,1,7,8,6,5] => 0010011 => 2

[[[[]],[[]]],[],[[]]] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,3,4,2,7,8,6,5] => 0010011 => 2

[[[[],[]],[]],[],[[]]] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => 1010011 => 2

[[[[[]]],[]],[],[[]]] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,2,4,3,7,8,6,5] => 0010011 => 2

[[[[],[],[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [3,2,1,4,7,8,6,5] => 1100011 => 2

[[[[],[[]]]],[],[[]]] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [2,3,1,4,7,8,6,5] => 0100011 => 2

[[[[[],[]]]],[],[[]]] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [2,1,3,4,7,8,6,5] => 1000011 => 2

[[[[[[]]]]],[],[[]]] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,2,3,4,7,8,6,5] => 0000011 => 2

[[[],[],[],[]],[[]],[]] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => 1110011 => 3

[[[],[],[[]]],[[]],[]] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => 0110011 => 2

[[[],[[]],[]],[[]],[]] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => 0110011 => 2

[[[],[[],[]]],[[]],[]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => 1010011 => 2

[[[],[[[]]]],[[]],[]] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => 0010011 => 2

[[[[]],[],[]],[[]],[]] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,4,3,2,6,8,7,5] => 0110011 => 2

[[[[]],[[]]],[[]],[]] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => 0010011 => 2

[[[[],[]],[]],[[]],[]] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => 1010011 => 2

[[[[[]]],[]],[[]],[]] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => 0010011 => 2

[[[[],[],[]]],[[]],[]] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => 1100011 => 2

[[[[[]],[]]],[[]],[]] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => 0100011 => 2

[[[[[[]]]]],[[]],[]] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => 0000011 => 2

[[[],[],[],[]],[[],[]]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => 1110101 => 3

[[[],[],[],[]],[[[]]]] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => 1110001 => 3

[[[],[],[[]]],[[],[]]] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => 0110101 => 2

[[[],[],[[]]],[[[]]]] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [3,4,2,1,6,7,8,5] => 0110001 => 2

[[[],[[]],[]],[[],[]]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => 0110101 => 2

[[[],[[]],[]],[[[]]]] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => 0110001 => 2

[[[],[[],[]]],[[],[]]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 1010101 => 1

[[[],[[],[]]],[[[]]]] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => 1010001 => 1

[[[],[[[]]]],[[],[]]] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => 0010101 => 1

[[[],[[[]]]],[[[]]]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => 0010001 => 1

[[[[]],[],[]],[[],[]]] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => 0110101 => 2

[[[[]],[],[]],[[[]]]] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,4,3,2,6,7,8,5] => 0110001 => 2

[[[[]],[[]]],[[],[]]] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => 0010101 => 1

[[[[]],[[]]],[[[]]]] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,3,4,2,6,7,8,5] => 0010001 => 1

[[[[],[]],[]],[[],[]]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => 1010101 => 1

[[[[],[]],[]],[[[]]]] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => 1010001 => 1

[[[[[]]],[]],[[],[]]] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => 0010101 => 1

[[[[[]]],[]],[[[]]]] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,2,4,3,6,7,8,5] => 0010001 => 1

[[[[],[],[]]],[[],[]]] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => 1100101 => 2

[[[[],[],[]]],[[[]]]] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [3,2,1,4,6,7,8,5] => 1100001 => 2

[[[[],[[]]]],[[],[]]] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => 0100101 => 1

[[[[],[[]]]],[[[]]]] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [2,3,1,4,6,7,8,5] => 0100001 => 1

[[[[[]],[]]],[[],[]]] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => 0100101 => 1

[[[[[]],[]]],[[[]]]] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,3,2,4,6,7,8,5] => 0100001 => 1

[[[[[],[]]]],[[],[]]] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => 1000101 => 1

[[[[[],[]]]],[[[]]]] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [2,1,3,4,6,7,8,5] => 1000001 => 1

[[[[[[]]]]],[[],[]]] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => 0000101 => 1

[[[[[[]]]]],[[[]]]] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => 0000001 => 1

[[[],[],[],[],[]],[],[]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 1111011 => 4

[[[],[],[],[[]]],[],[]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [4,5,3,2,1,8,7,6] => 0111011 => 3

[[[],[],[[]],[]],[],[]] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [3,5,4,2,1,8,7,6] => 0111011 => 3

[[[],[],[[],[]]],[],[]] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [4,3,5,2,1,8,7,6] => 1011011 => 2

[[[],[],[[[]]]],[],[]] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [3,4,5,2,1,8,7,6] => 0011011 => 2

[[[],[[]],[],[]],[],[]] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [2,5,4,3,1,8,7,6] => 0111011 => 3

[[[],[[]],[[]]],[],[]] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [2,4,5,3,1,8,7,6] => 0011011 => 2

[[[],[[],[]],[]],[],[]] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => 1011011 => 2

[[[],[[[]]],[]],[],[]] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [2,3,5,4,1,8,7,6] => 0011011 => 2

[[[],[[],[],[]]],[],[]] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => 1101011 => 2

[[[],[[],[[]]]],[],[]] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => 0101011 => 2

[[[],[[[]],[]]],[],[]] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [2,4,3,5,1,8,7,6] => 0101011 => 2

[[[],[[[],[]]]],[],[]] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [3,2,4,5,1,8,7,6] => 1001011 => 2

[[[],[[[[]]]]],[],[]] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [2,3,4,5,1,8,7,6] => 0001011 => 2

[[[[]],[],[],[]],[],[]] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,5,4,3,2,8,7,6] => 0111011 => 3

[[[[]],[],[[]]],[],[]] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,4,5,3,2,8,7,6] => 0011011 => 2

[[[[]],[[],[]]],[],[]] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,4,3,5,2,8,7,6] => 0101011 => 2

[[[[]],[[[]]]],[],[]] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,3,4,5,2,8,7,6] => 0001011 => 2

[[[[],[]],[],[]],[],[]] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [2,1,5,4,3,8,7,6] => 1011011 => 2

[[[[[]]],[],[]],[],[]] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,2,5,4,3,8,7,6] => 0011011 => 2

[[[[],[]],[[]]],[],[]] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [2,1,4,5,3,8,7,6] => 1001011 => 2

[[[[[]]],[[]]],[],[]] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => 0001011 => 2

[[[[[]],[]],[]],[],[]] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,3,2,5,4,8,7,6] => 0101011 => 2

[[[[[],[]]],[]],[],[]] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [2,1,3,5,4,8,7,6] => 1001011 => 2

[[[[[[]]]],[]],[],[]] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,2,3,5,4,8,7,6] => 0001011 => 2

[[[[],[],[],[]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => 1110011 => 3

[[[[],[[]],[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [2,4,3,1,5,8,7,6] => 0110011 => 2

[[[[],[[],[]]]],[],[]] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => 1010011 => 2

[[[[],[[[]]]]],[],[]] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [2,3,4,1,5,8,7,6] => 0010011 => 2

[[[[[]],[],[]]],[],[]] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,4,3,2,5,8,7,6] => 0110011 => 2

[[[[[]],[[]]]],[],[]] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,3,4,2,5,8,7,6] => 0010011 => 2

[[[[[],[]],[]]],[],[]] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => 1010011 => 2

[[[[[[]]],[]]],[],[]] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,2,4,3,5,8,7,6] => 0010011 => 2

[[[[[],[],[]]]],[],[]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 1100011 => 2

[[[[[[]],[]]]],[],[]] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,3,2,4,5,8,7,6] => 0100011 => 2

[[[[[[],[]]]]],[],[]] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [2,1,3,4,5,8,7,6] => 1000011 => 2

[[[[[[[]]]]]],[],[]] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => 0000011 => 2

[[[],[],[],[],[]],[[]]] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => 1111001 => 4

[[[],[],[[]],[]],[[]]] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [3,5,4,2,1,7,8,6] => 0111001 => 3

[[[],[],[[[]]]],[[]]] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [3,4,5,2,1,7,8,6] => 0011001 => 2

[[[],[[]],[],[]],[[]]] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [2,5,4,3,1,7,8,6] => 0111001 => 3

[[[],[[]],[[]]],[[]]] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => 0011001 => 2

[[[],[[],[]],[]],[[]]] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => 1011001 => 2

[[[],[[],[],[]]],[[]]] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => 1101001 => 2

[[[],[[],[[]]]],[[]]] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => 0101001 => 1

[[[],[[[]],[]]],[[]]] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => 0101001 => 1

[[[],[[[[]]]]],[[]]] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => 0001001 => 1

[[[[]],[],[],[]],[[]]] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,5,4,3,2,7,8,6] => 0111001 => 3

[[[[]],[],[[]]],[[]]] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,4,5,3,2,7,8,6] => 0011001 => 2

[[[[]],[[]],[]],[[]]] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,3,5,4,2,7,8,6] => 0011001 => 2

[[[[]],[[],[]]],[[]]] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,4,3,5,2,7,8,6] => 0101001 => 1

[[[[]],[[[]]]],[[]]] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,3,4,5,2,7,8,6] => 0001001 => 1

[[[[[]]],[],[]],[[]]] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,2,5,4,3,7,8,6] => 0011001 => 2

[[[[[]]],[[]]],[[]]] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,2,4,5,3,7,8,6] => 0001001 => 1

[[[[[]],[]],[]],[[]]] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,3,2,5,4,7,8,6] => 0101001 => 1

[[[[[],[]]],[]],[[]]] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [2,1,3,5,4,7,8,6] => 1001001 => 1

[[[[[[]]]],[]],[[]]] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,2,3,5,4,7,8,6] => 0001001 => 1

[[[[],[],[],[]]],[[]]] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => 1110001 => 3

[[[[],[[],[]]]],[[]]] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => 1010001 => 1

[[[[],[[[]]]]],[[]]] => [[[.,[[[.,.],.],.]],.],[[.,.],.]] => [2,3,4,1,5,7,8,6] => 0010001 => 1

[[[[[]],[],[]]],[[]]] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,4,3,2,5,7,8,6] => 0110001 => 2

[[[[[]],[[]]]],[[]]] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,3,4,2,5,7,8,6] => 0010001 => 1

[[[[[],[]],[]]],[[]]] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [2,1,4,3,5,7,8,6] => 1010001 => 1

[[[[[[]]],[]]],[[]]] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,2,4,3,5,7,8,6] => 0010001 => 1

[[[[[],[],[]]]],[[]]] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [3,2,1,4,5,7,8,6] => 1100001 => 2

[[[[[],[[]]]]],[[]]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => 0100001 => 1

[[[[[[]],[]]]],[[]]] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,3,2,4,5,7,8,6] => 0100001 => 1

[[[[[[],[]]]]],[[]]] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [2,1,3,4,5,7,8,6] => 1000001 => 1

[[[[[[[]]]]]],[[]]] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => 0000001 => 1

[[[],[],[],[],[],[]],[]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => 1111101 => 5

[[[],[],[],[],[[]]],[]] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [5,6,4,3,2,1,8,7] => 0111101 => 4

[[[],[],[],[[]],[]],[]] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [4,6,5,3,2,1,8,7] => 0111101 => 4

[[[],[],[],[[],[]]],[]] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => 1011101 => 3

[[[],[],[],[[[]]]],[]] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => 0011101 => 3

[[[],[],[[]],[],[]],[]] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [3,6,5,4,2,1,8,7] => 0111101 => 4

[[[],[],[[]],[[]]],[]] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => 0011101 => 3

[[[],[],[[],[]],[]],[]] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [4,3,6,5,2,1,8,7] => 1011101 => 3

[[[],[],[[[]]],[]],[]] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [3,4,6,5,2,1,8,7] => 0011101 => 3

[[[],[],[[],[],[]]],[]] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [5,4,3,6,2,1,8,7] => 1101101 => 2

[[[],[],[[],[[]]]],[]] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [4,5,3,6,2,1,8,7] => 0101101 => 2

[[[],[],[[[],[]]]],[]] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [4,3,5,6,2,1,8,7] => 1001101 => 2

[[[],[],[[[[]]]]],[]] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [3,4,5,6,2,1,8,7] => 0001101 => 2

[[[],[[]],[],[],[]],[]] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [2,6,5,4,3,1,8,7] => 0111101 => 4

[[[],[[]],[],[[]]],[]] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [2,5,6,4,3,1,8,7] => 0011101 => 3

[[[],[[]],[[]],[]],[]] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => 0011101 => 3

[[[],[[],[]],[],[]],[]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => 1011101 => 3

[[[],[[[]]],[],[]],[]] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [2,3,6,5,4,1,8,7] => 0011101 => 3

[[[],[[],[]],[[]]],[]] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [3,2,5,6,4,1,8,7] => 1001101 => 2

[[[],[[[]]],[[]]],[]] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [2,3,5,6,4,1,8,7] => 0001101 => 2

[[[],[[],[],[]],[]],[]] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [4,3,2,6,5,1,8,7] => 1101101 => 2

[[[],[[],[[]]],[]],[]] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [3,4,2,6,5,1,8,7] => 0101101 => 2

[[[],[[[]],[]],[]],[]] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => 0101101 => 2

[[[],[[],[],[],[]]],[]] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [5,4,3,2,6,1,8,7] => 1110101 => 3

[[[],[[],[],[[]]]],[]] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [4,5,3,2,6,1,8,7] => 0110101 => 2

[[[],[[],[[]],[]]],[]] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [3,5,4,2,6,1,8,7] => 0110101 => 2

[[[],[[],[[],[]]]],[]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => 1010101 => 1

[[[],[[],[[[]]]]],[]] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [3,4,5,2,6,1,8,7] => 0010101 => 1

[[[],[[[]],[],[]]],[]] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [2,5,4,3,6,1,8,7] => 0110101 => 2

[[[],[[[]],[[]]]],[]] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [2,4,5,3,6,1,8,7] => 0010101 => 1

[[[],[[[],[]],[]]],[]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => 1010101 => 1

[[[],[[[],[],[]]]],[]] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [4,3,2,5,6,1,8,7] => 1100101 => 2

[[[],[[[],[[]]]]],[]] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [3,4,2,5,6,1,8,7] => 0100101 => 1

[[[],[[[[]],[]]]],[]] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [2,4,3,5,6,1,8,7] => 0100101 => 1

[[[],[[[[[]]]]]],[]] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => 0000101 => 1

[[[[]],[],[],[],[]],[]] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,6,5,4,3,2,8,7] => 0111101 => 4

[[[[]],[],[],[[]]],[]] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,5,6,4,3,2,8,7] => 0011101 => 3

[[[[]],[],[[],[]]],[]] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,5,4,6,3,2,8,7] => 0101101 => 2

[[[[]],[[]],[],[]],[]] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,3,6,5,4,2,8,7] => 0011101 => 3

[[[[]],[[[[]]]]],[]] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,3,4,5,6,2,8,7] => 0000101 => 1

[[[[],[]],[],[],[]],[]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 1011101 => 3

[[[[],[]],[],[[]]],[]] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => 1001101 => 2

[[[[],[]],[[]],[]],[]] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => 1001101 => 2

[[[[],[]],[[],[]]],[]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 1010101 => 1

[[[[],[]],[[[]]]],[]] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => 1000101 => 1

[[[[[]]],[[[]]]],[]] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,2,4,5,6,3,8,7] => 0000101 => 1

[[[[],[],[]],[],[]],[]] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [3,2,1,6,5,4,8,7] => 1101101 => 2

[[[[],[[]]],[],[]],[]] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [2,3,1,6,5,4,8,7] => 0101101 => 2

[[[[[]],[]],[],[]],[]] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,3,2,6,5,4,8,7] => 0101101 => 2

[[[[[[]]]],[],[]],[]] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,2,3,6,5,4,8,7] => 0001101 => 2

[[[[[]],[]],[[]]],[]] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,3,2,5,6,4,8,7] => 0100101 => 1

[[[[[],[]]],[[]]],[]] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [2,1,3,5,6,4,8,7] => 1000101 => 1

[[[[[[]]]],[[]]],[]] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,2,3,5,6,4,8,7] => 0000101 => 1

[[[[],[],[],[]],[]],[]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => 1110101 => 3

[[[[],[],[[]]],[]],[]] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => 0110101 => 2

[[[[],[[]],[]],[]],[]] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => 0110101 => 2

[[[[],[[],[]]],[]],[]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => 1010101 => 1

[[[[],[[[]]]],[]],[]] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => 0010101 => 1

[[[[[]],[[]]],[]],[]] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,3,4,2,6,5,8,7] => 0010101 => 1

[[[[[],[]],[]],[]],[]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => 1010101 => 1

[[[[[[]]],[]],[]],[]] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,2,4,3,6,5,8,7] => 0010101 => 1

[[[[[],[[]]]],[]],[]] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [2,3,1,4,6,5,8,7] => 0100101 => 1

[[[[[[]],[]]],[]],[]] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,3,2,4,6,5,8,7] => 0100101 => 1

[[[[[[],[]]]],[]],[]] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [2,1,3,4,6,5,8,7] => 1000101 => 1

[[[[[[[]]]]],[]],[]] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,2,3,4,6,5,8,7] => 0000101 => 1

[[[[],[],[],[],[]]],[]] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [5,4,3,2,1,6,8,7] => 1111001 => 4

[[[[],[],[],[[]]]],[]] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [4,5,3,2,1,6,8,7] => 0111001 => 3

[[[[],[],[[]],[]]],[]] => [[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [3,5,4,2,1,6,8,7] => 0111001 => 3

[[[[],[],[[],[]]]],[]] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [4,3,5,2,1,6,8,7] => 1011001 => 2

[[[[],[],[[[]]]]],[]] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [3,4,5,2,1,6,8,7] => 0011001 => 2

[[[[],[[]],[],[]]],[]] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [2,5,4,3,1,6,8,7] => 0111001 => 3

[[[[],[[]],[[]]]],[]] => [[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [2,4,5,3,1,6,8,7] => 0011001 => 2

[[[[],[[],[]],[]]],[]] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [3,2,5,4,1,6,8,7] => 1011001 => 2

[[[[],[[[]]],[]]],[]] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [2,3,5,4,1,6,8,7] => 0011001 => 2

[[[[],[[[]],[]]]],[]] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [2,4,3,5,1,6,8,7] => 0101001 => 1

[[[[],[[[[]]]]]],[]] => [[[.,[[[[.,.],.],.],.]],.],[.,.]] => [2,3,4,5,1,6,8,7] => 0001001 => 1

[[[[[]],[],[[]]]],[]] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,4,5,3,2,6,8,7] => 0011001 => 2

[[[[[]],[[]],[]]],[]] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,3,5,4,2,6,8,7] => 0011001 => 2

[[[[[]],[[[]]]]],[]] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,3,4,5,2,6,8,7] => 0001001 => 1

[[[[[[]]],[],[]]],[]] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,2,5,4,3,6,8,7] => 0011001 => 2

[[[[[],[]],[[]]]],[]] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => 1001001 => 1

[[[[[[],[]]],[]]],[]] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [2,1,3,5,4,6,8,7] => 1001001 => 1

[[[[[[[]]]],[]]],[]] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,2,3,5,4,6,8,7] => 0001001 => 1

[[[[[],[],[],[]]]],[]] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => 1110001 => 3

[[[[[],[[],[]]]]],[]] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => 1010001 => 1

[[[[[],[[[]]]]]],[]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [2,3,4,1,5,6,8,7] => 0010001 => 1

[[[[[[]],[],[]]]],[]] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,4,3,2,5,6,8,7] => 0110001 => 2

[[[[[[]],[[]]]]],[]] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,3,4,2,5,6,8,7] => 0010001 => 1

[[[[[[],[]],[]]]],[]] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [2,1,4,3,5,6,8,7] => 1010001 => 1

[[[[[[[]]],[]]]],[]] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,2,4,3,5,6,8,7] => 0010001 => 1

[[[[[[],[],[]]]]],[]] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [3,2,1,4,5,6,8,7] => 1100001 => 2

[[[[[[],[[]]]]]],[]] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [2,3,1,4,5,6,8,7] => 0100001 => 1

[[[[[[[]],[]]]]],[]] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,3,2,4,5,6,8,7] => 0100001 => 1

[[[[[[[],[]]]]]],[]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => 1000001 => 1

[[[[[[[[]]]]]]],[]] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => 0000001 => 1

[[[],[],[],[],[],[],[]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 1111110 => 6

[[[],[],[],[],[],[[]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 0111110 => 5

[[[],[],[],[],[[]],[]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 0111110 => 5

[[[],[],[],[],[[],[]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 1011110 => 4

[[[],[],[],[],[[[]]]]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 0011110 => 4

[[[],[],[],[[]],[],[]]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => 0111110 => 5

[[[],[],[],[[]],[[]]]] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [4,6,7,5,3,2,1,8] => 0011110 => 4

[[[],[],[],[[],[]],[]]] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [5,4,7,6,3,2,1,8] => 1011110 => 4

[[[],[],[],[[[]]],[]]] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [4,5,7,6,3,2,1,8] => 0011110 => 4

[[[],[],[],[[],[],[]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 1101110 => 3

[[[],[],[],[[],[[]]]]] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => 0101110 => 3

[[[],[],[],[[[]],[]]]] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [4,6,5,7,3,2,1,8] => 0101110 => 3

[[[],[],[],[[[],[]]]]] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => 1001110 => 3

[[[],[],[],[[[[]]]]]] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => 0001110 => 3

[[[],[],[[]],[[]],[]]] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [3,5,7,6,4,2,1,8] => 0011110 => 4

[[[],[],[[]],[[[]]]]] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [3,5,6,7,4,2,1,8] => 0001110 => 3

[[[],[],[[],[]],[],[]]] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [4,3,7,6,5,2,1,8] => 1011110 => 4

[[[],[],[[[]]],[],[]]] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [3,4,7,6,5,2,1,8] => 0011110 => 4

[[[],[],[[],[],[]],[]]] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [5,4,3,7,6,2,1,8] => 1101110 => 3

[[[],[],[[],[[]]],[]]] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [4,5,3,7,6,2,1,8] => 0101110 => 3

[[[],[],[[[]],[]],[]]] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [3,5,4,7,6,2,1,8] => 0101110 => 3

[[[],[],[[[],[]]],[]]] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [4,3,5,7,6,2,1,8] => 1001110 => 3

[[[],[],[[],[],[],[]]]] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => 1110110 => 3

[[[],[],[[],[],[[]]]]] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => 0110110 => 2

[[[],[],[[],[[],[]]]]] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => 1010110 => 2

[[[],[],[[[]],[],[]]]] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [3,6,5,4,7,2,1,8] => 0110110 => 2

[[[],[],[[[]],[[]]]]] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [3,5,6,4,7,2,1,8] => 0010110 => 2

[[[],[],[[[],[]],[]]]] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [4,3,6,5,7,2,1,8] => 1010110 => 2

[[[],[],[[[],[],[]]]]] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => 1100110 => 2

[[[],[],[[[[[]]]]]]] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => 0000110 => 2

[[[],[[]],[],[],[],[]]] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => 0111110 => 5

[[[],[[]],[],[],[[]]]] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [2,6,7,5,4,3,1,8] => 0011110 => 4

[[[],[[]],[],[[]],[]]] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [2,5,7,6,4,3,1,8] => 0011110 => 4

[[[],[[]],[],[[[]]]]] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [2,5,6,7,4,3,1,8] => 0001110 => 3

[[[],[[]],[[]],[[]]]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => 0001110 => 3

[[[],[[]],[[],[]],[]]] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [2,5,4,7,6,3,1,8] => 0101110 => 3

[[[],[[]],[[],[[]]]]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => 0010110 => 2

[[[],[[]],[[[],[]]]]] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [2,5,4,6,7,3,1,8] => 0100110 => 2

[[[],[[]],[[[[]]]]]] => [[.,[[.,.],[[[[.,.],.],.],.]]],.] => [2,4,5,6,7,3,1,8] => 0000110 => 2

[[[],[[],[]],[],[],[]]] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => 1011110 => 4

[[[],[[[]]],[],[],[]]] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [2,3,7,6,5,4,1,8] => 0011110 => 4

[[[],[[],[]],[],[[]]]] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [3,2,6,7,5,4,1,8] => 1001110 => 3

[[[],[[[]]],[],[[]]]] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [2,3,6,7,5,4,1,8] => 0001110 => 3

[[[],[[],[]],[[]],[]]] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [3,2,5,7,6,4,1,8] => 1001110 => 3

[[[],[[[]]],[[]],[]]] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [2,3,5,7,6,4,1,8] => 0001110 => 3

[[[],[[],[]],[[],[]]]] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [3,2,6,5,7,4,1,8] => 1010110 => 2

[[[],[[],[]],[[[]]]]] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [3,2,5,6,7,4,1,8] => 1000110 => 2

[[[],[[[]]],[[],[]]]] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [2,3,6,5,7,4,1,8] => 0010110 => 2

[[[],[[[]]],[[[]]]]] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [2,3,5,6,7,4,1,8] => 0000110 => 2

[[[],[[],[[]]],[],[]]] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [3,4,2,7,6,5,1,8] => 0101110 => 3

[[[],[[[[]]]],[],[]]] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [2,3,4,7,6,5,1,8] => 0001110 => 3

[[[],[[],[],[]],[[]]]] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [4,3,2,6,7,5,1,8] => 1100110 => 2

[[[],[[],[[]]],[[]]]] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [3,4,2,6,7,5,1,8] => 0100110 => 2

[[[],[[[],[]]],[[]]]] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [3,2,4,6,7,5,1,8] => 1000110 => 2

[[[],[[[[]]]],[[]]]] => [[.,[[[[.,.],.],.],[[.,.],.]]],.] => [2,3,4,6,7,5,1,8] => 0000110 => 2

[[[],[[],[],[],[]],[]]] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 1110110 => 3

[[[],[[],[],[[]]],[]]] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [4,5,3,2,7,6,1,8] => 0110110 => 2

[[[],[[],[[]],[]],[]]] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [3,5,4,2,7,6,1,8] => 0110110 => 2

[[[],[[],[[],[]]],[]]] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [4,3,5,2,7,6,1,8] => 1010110 => 2

[[[],[[],[[[]]]],[]]] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [3,4,5,2,7,6,1,8] => 0010110 => 2

[[[],[[[],[]],[]],[]]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 1010110 => 2

[[[],[[[],[],[]]],[]]] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [4,3,2,5,7,6,1,8] => 1100110 => 2

[[[],[[[],[[]]]],[]]] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [3,4,2,5,7,6,1,8] => 0100110 => 2

[[[],[[[[[]]]]],[]]] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [2,3,4,5,7,6,1,8] => 0000110 => 2

[[[],[[],[],[],[],[]]]] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => 1111010 => 4

[[[],[[],[],[],[[]]]]] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => 0111010 => 3

[[[],[[],[],[[],[]]]]] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => 1011010 => 2

[[[],[[],[[]],[],[]]]] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [3,6,5,4,2,7,1,8] => 0111010 => 3

[[[],[[],[[]],[[]]]]] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [3,5,6,4,2,7,1,8] => 0011010 => 2

[[[],[[],[[[]]],[]]]] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [3,4,6,5,2,7,1,8] => 0011010 => 2

[[[],[[],[[],[],[]]]]] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => 1101010 => 2

[[[],[[],[[],[[]]]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => 0101010 => 1

[[[],[[],[[[]],[]]]]] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => 0101010 => 1

[[[],[[],[[[],[]]]]]] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => 1001010 => 1

[[[],[[],[[[[]]]]]]] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => 0001010 => 1

[[[],[[[]],[[],[]]]]] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [2,5,4,6,3,7,1,8] => 0101010 => 1

[[[],[[[],[]],[],[]]]] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [3,2,6,5,4,7,1,8] => 1011010 => 2

[[[],[[[[]]],[[]]]]] => [[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => 0001010 => 1

[[[],[[[],[],[]],[]]]] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [4,3,2,6,5,7,1,8] => 1101010 => 2

[[[],[[[],[[]]],[]]]] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [3,4,2,6,5,7,1,8] => 0101010 => 1

[[[],[[[[]],[]],[]]]] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [2,4,3,6,5,7,1,8] => 0101010 => 1

[[[],[[[[[]]]],[]]]] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => 0001010 => 1

[[[],[[[],[],[],[]]]]] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => 1110010 => 3

[[[],[[[],[[]],[]]]]] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [3,5,4,2,6,7,1,8] => 0110010 => 2

[[[],[[[],[[[]]]]]]] => [[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => 0010010 => 1

[[[],[[[[]],[],[]]]]] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [2,5,4,3,6,7,1,8] => 0110010 => 2

[[[],[[[[]],[[]]]]]] => [[.,[[[[.,.],[[.,.],.]],.],.]],.] => [2,4,5,3,6,7,1,8] => 0010010 => 1

[[[],[[[[[]]],[]]]]] => [[.,[[[[[.,.],.],[.,.]],.],.]],.] => [2,3,5,4,6,7,1,8] => 0010010 => 1

[[[],[[[[],[],[]]]]]] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => 1100010 => 2

[[[],[[[[],[[]]]]]]] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => 0100010 => 1

[[[],[[[[[],[]]]]]]] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => 1000010 => 1

[[[],[[[[[[]]]]]]]] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 0000010 => 1

[[[[]],[],[],[],[],[]]] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8] => 0111110 => 5

[[[[]],[],[],[],[[]]]] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => 0011110 => 4

[[[[]],[],[],[[],[]]]] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,6,5,7,4,3,2,8] => 0101110 => 3

[[[[]],[],[],[[[]]]]] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,5,6,7,4,3,2,8] => 0001110 => 3

[[[[]],[],[[]],[],[]]] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,4,7,6,5,3,2,8] => 0011110 => 4

[[[[]],[],[[]],[[]]]] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,4,6,7,5,3,2,8] => 0001110 => 3

[[[[]],[],[[],[]],[]]] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,5,4,7,6,3,2,8] => 0101110 => 3

[[[[]],[],[[],[[]]]]] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,5,6,4,7,3,2,8] => 0010110 => 2

[[[[]],[],[[[]],[]]]] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,4,6,5,7,3,2,8] => 0010110 => 2

[[[[]],[],[[[],[]]]]] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,5,4,6,7,3,2,8] => 0100110 => 2

[[[[]],[],[[[[]]]]]] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => 0000110 => 2

[[[[]],[[]],[],[],[]]] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,3,7,6,5,4,2,8] => 0011110 => 4

[[[[]],[[]],[],[[]]]] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,3,6,7,5,4,2,8] => 0001110 => 3

[[[[]],[[]],[[]],[]]] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,3,5,7,6,4,2,8] => 0001110 => 3

[[[[]],[[]],[[],[]]]] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,3,6,5,7,4,2,8] => 0010110 => 2

[[[[]],[[]],[[[]]]]] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,3,5,6,7,4,2,8] => 0000110 => 2

[[[[]],[[[]]],[[]]]] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,3,4,6,7,5,2,8] => 0000110 => 2

[[[[]],[[[]],[]],[]]] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,3,5,4,7,6,2,8] => 0010110 => 2

[[[[]],[[[],[]]],[]]] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,4,3,5,7,6,2,8] => 0100110 => 2

[[[[]],[[[[]]]],[]]] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,3,4,5,7,6,2,8] => 0000110 => 2

[[[[]],[[],[[],[]]]]] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,5,4,6,3,7,2,8] => 0101010 => 1

[[[[]],[[],[[[]]]]]] => [[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,4,5,6,3,7,2,8] => 0001010 => 1

[[[[]],[[[]],[],[]]]] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,3,6,5,4,7,2,8] => 0011010 => 2

[[[[]],[[[]],[[]]]]] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,3,5,6,4,7,2,8] => 0001010 => 1

[[[[]],[[[],[]],[]]]] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,4,3,6,5,7,2,8] => 0101010 => 1

[[[[]],[[[[]]],[]]]] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,3,4,6,5,7,2,8] => 0001010 => 1

[[[[]],[[[],[],[]]]]] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,5,4,3,6,7,2,8] => 0110010 => 2

[[[[]],[[[],[[]]]]]] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,4,5,3,6,7,2,8] => 0010010 => 1

[[[[]],[[[[]],[]]]]] => [[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,3,5,4,6,7,2,8] => 0010010 => 1

[[[[]],[[[[[]]]]]]] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,3,4,5,6,7,2,8] => 0000010 => 1

[[[[],[]],[],[],[],[]]] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8] => 1011110 => 4

[[[[[]]],[],[],[],[]]] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8] => 0011110 => 4

[[[[],[]],[],[],[[]]]] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [2,1,6,7,5,4,3,8] => 1001110 => 3

[[[[[]]],[],[],[[]]]] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,2,6,7,5,4,3,8] => 0001110 => 3

[[[[[]]],[],[[]],[]]] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,2,5,7,6,4,3,8] => 0001110 => 3

[[[[],[]],[],[[[]]]]] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [2,1,5,6,7,4,3,8] => 1000110 => 2

[[[[[]]],[],[[[]]]]] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,2,5,6,7,4,3,8] => 0000110 => 2

[[[[],[]],[[]],[[]]]] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [2,1,4,6,7,5,3,8] => 1000110 => 2

[[[[[]]],[[]],[[]]]] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,2,4,6,7,5,3,8] => 0000110 => 2

[[[[],[]],[[[[]]]]]] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [2,1,4,5,6,7,3,8] => 1000010 => 1

[[[[[]]],[[],[[]]]]] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,2,5,6,4,7,3,8] => 0001010 => 1

[[[[[]]],[[[],[]]]]] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,2,5,4,6,7,3,8] => 0010010 => 1

[[[[[]]],[[[[]]]]]] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,2,4,5,6,7,3,8] => 0000010 => 1

[[[[],[],[]],[],[],[]]] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => 1101110 => 3

[[[[[]],[]],[],[],[]]] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,3,2,7,6,5,4,8] => 0101110 => 3

[[[[[[]]]],[],[],[]]] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8] => 0001110 => 3

[[[[],[],[]],[],[[]]]] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [3,2,1,6,7,5,4,8] => 1100110 => 2

[[[[],[[]]],[],[[]]]] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [2,3,1,6,7,5,4,8] => 0100110 => 2

[[[[[]],[]],[],[[]]]] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,3,2,6,7,5,4,8] => 0100110 => 2

[[[[[],[]]],[],[[]]]] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [2,1,3,6,7,5,4,8] => 1000110 => 2

[[[[[[]]]],[],[[]]]] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,2,3,6,7,5,4,8] => 0000110 => 2

[[[[],[],[]],[[]],[]]] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [3,2,1,5,7,6,4,8] => 1100110 => 2

[[[[[]],[]],[[]],[]]] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,3,2,5,7,6,4,8] => 0100110 => 2

[[[[[[]]]],[[]],[]]] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,2,3,5,7,6,4,8] => 0000110 => 2

[[[[],[],[]],[[[]]]]] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [3,2,1,5,6,7,4,8] => 1100010 => 2

[[[[],[[]]],[[],[]]]] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [2,3,1,6,5,7,4,8] => 0101010 => 1

[[[[],[[]]],[[[]]]]] => [[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => 0100010 => 1

[[[[[]],[]],[[],[]]]] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,3,2,6,5,7,4,8] => 0101010 => 1

[[[[[]],[]],[[[]]]]] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,3,2,5,6,7,4,8] => 0100010 => 1

[[[[[[]]]],[[],[]]]] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,2,3,6,5,7,4,8] => 0001010 => 1

[[[[[[]]]],[[[]]]]] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => 0000010 => 1

[[[[],[],[],[]],[],[]]] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => 1110110 => 3

[[[[],[[],[]]],[],[]]] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => 1010110 => 2

[[[[],[[[]]]],[],[]]] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8] => 0010110 => 2

[[[[[]],[],[]],[],[]]] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 0110110 => 2

[[[[[],[],[]]],[],[]]] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8] => 1100110 => 2

[[[[[[]],[]]],[],[]]] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8] => 0100110 => 2

[[[[[[[]]]]],[],[]]] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8] => 0000110 => 2

[[[[],[],[],[]],[[]]]] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => 1110010 => 3

[[[[],[[],[]]],[[]]]] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => 1010010 => 1

[[[[],[[[]]]],[[]]]] => [[[.,[[[.,.],.],.]],[[.,.],.]],.] => [2,3,4,1,6,7,5,8] => 0010010 => 1

[[[[[]],[],[]],[[]]]] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,4,3,2,6,7,5,8] => 0110010 => 2

[[[[[]],[[]]],[[]]]] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => 0010010 => 1

[[[[[[]]],[]],[[]]]] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,2,4,3,6,7,5,8] => 0010010 => 1

[[[[[],[[]]]],[[]]]] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => 0100010 => 1

[[[[[[],[]]]],[[]]]] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [2,1,3,4,6,7,5,8] => 1000010 => 1

[[[[[[[]]]]],[[]]]] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,2,3,4,6,7,5,8] => 0000010 => 1

[[[[],[],[],[],[]],[]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8] => 1111010 => 4

[[[[],[],[],[[]]],[]]] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [4,5,3,2,1,7,6,8] => 0111010 => 3

[[[[],[],[[]],[]],[]]] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [3,5,4,2,1,7,6,8] => 0111010 => 3

[[[[],[],[[[]]]],[]]] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [3,4,5,2,1,7,6,8] => 0011010 => 2

[[[[],[[]],[],[]],[]]] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [2,5,4,3,1,7,6,8] => 0111010 => 3

[[[[],[[]],[[]]],[]]] => [[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [2,4,5,3,1,7,6,8] => 0011010 => 2

[[[[],[[],[]],[]],[]]] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [3,2,5,4,1,7,6,8] => 1011010 => 2

[[[[],[[[]]],[]],[]]] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [2,3,5,4,1,7,6,8] => 0011010 => 2

[[[[],[[],[[]]]],[]]] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => 0101010 => 1

[[[[],[[[]],[]]],[]]] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => 0101010 => 1

[[[[],[[[[]]]]],[]]] => [[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8] => 0001010 => 1

[[[[[]],[],[],[]],[]]] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,5,4,3,2,7,6,8] => 0111010 => 3

[[[[[]],[],[[]]],[]]] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,4,5,3,2,7,6,8] => 0011010 => 2

[[[[[]],[[]],[]],[]]] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,3,5,4,2,7,6,8] => 0011010 => 2

[[[[[]],[[],[]]],[]]] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,4,3,5,2,7,6,8] => 0101010 => 1

[[[[[]],[[[]]]],[]]] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,3,4,5,2,7,6,8] => 0001010 => 1

[[[[[],[]],[],[]],[]]] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [2,1,5,4,3,7,6,8] => 1011010 => 2

[[[[[[]]],[[]]],[]]] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,2,4,5,3,7,6,8] => 0001010 => 1

[[[[[],[],[]],[]],[]]] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => 1101010 => 2

[[[[[],[[]]],[]],[]]] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => 0101010 => 1

[[[[[[]],[]],[]],[]]] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => 0101010 => 1

[[[[[[[]]]],[]],[]]] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => 0001010 => 1

[[[[[],[],[],[]]],[]]] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => 1110010 => 3

[[[[[],[[],[]]]],[]]] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => 1010010 => 1

[[[[[],[[[]]]]],[]]] => [[[[.,[[[.,.],.],.]],.],[.,.]],.] => [2,3,4,1,5,7,6,8] => 0010010 => 1

[[[[[[]],[],[]]],[]]] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8] => 0110010 => 2

[[[[[[]],[[]]]],[]]] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,3,4,2,5,7,6,8] => 0010010 => 1

[[[[[[[]]],[]]],[]]] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8] => 0010010 => 1

[[[[[[],[[]]]]],[]]] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8] => 0100010 => 1

[[[[[[[]],[]]]],[]]] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => 0100010 => 1

[[[[[[[],[]]]]],[]]] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8] => 1000010 => 1

[[[[[[[[]]]]]],[]]] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => 0000010 => 1

[[[[],[],[],[],[],[]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 1111100 => 5

[[[[],[],[],[],[[]]]]] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => 0111100 => 4

[[[[],[],[],[[],[]]]]] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => 1011100 => 3

[[[[],[],[],[[[]]]]]] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => 0011100 => 3

[[[[],[],[[]],[],[]]]] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [3,6,5,4,2,1,7,8] => 0111100 => 4

[[[[],[],[[],[]],[]]]] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [4,3,6,5,2,1,7,8] => 1011100 => 3

[[[[],[],[[],[],[]]]]] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => 1101100 => 2

[[[[],[],[[[[]]]]]]] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => 0001100 => 2

[[[[],[[]],[[]],[]]]] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [2,4,6,5,3,1,7,8] => 0011100 => 3

[[[[],[[]],[[[]]]]]] => [[[.,[[.,.],[[[.,.],.],.]]],.],.] => [2,4,5,6,3,1,7,8] => 0001100 => 2

[[[[],[[[]]],[],[]]]] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => 0011100 => 3

[[[[],[[[]]],[[]]]]] => [[[.,[[[.,.],.],[[.,.],.]]],.],.] => [2,3,5,6,4,1,7,8] => 0001100 => 2

[[[[],[[],[],[]],[]]]] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [4,3,2,6,5,1,7,8] => 1101100 => 2

[[[[],[[[]],[]],[]]]] => [[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => 0101100 => 2

[[[[],[[[[]]]],[]]]] => [[[.,[[[[.,.],.],.],[.,.]]],.],.] => [2,3,4,6,5,1,7,8] => 0001100 => 2

[[[[],[[],[],[],[]]]]] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => 1110100 => 3

[[[[],[[],[],[[]]]]]] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => 0110100 => 2

[[[[],[[],[[]],[]]]]] => [[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [3,5,4,2,6,1,7,8] => 0110100 => 2

[[[[],[[],[[],[]]]]]] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => 1010100 => 1

[[[[],[[],[[[]]]]]]] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => 0010100 => 1

[[[[],[[[[]]],[]]]]] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => 0010100 => 1

[[[[],[[[],[],[]]]]]] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => 1100100 => 2

[[[[],[[[],[[]]]]]]] => [[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => 0100100 => 1

[[[[],[[[[],[]]]]]]] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => 1000100 => 1

[[[[],[[[[[]]]]]]]] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 0000100 => 1

[[[[[]],[],[],[],[]]]] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,6,5,4,3,2,7,8] => 0111100 => 4

[[[[[]],[],[],[[]]]]] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,5,6,4,3,2,7,8] => 0011100 => 3

[[[[[]],[],[[]],[]]]] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,4,6,5,3,2,7,8] => 0011100 => 3

[[[[[]],[],[[],[]]]]] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,5,4,6,3,2,7,8] => 0101100 => 2

[[[[[]],[],[[[]]]]]] => [[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,4,5,6,3,2,7,8] => 0001100 => 2

[[[[[]],[[]],[[]]]]] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,3,5,6,4,2,7,8] => 0001100 => 2

[[[[[]],[[],[]],[]]]] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,4,3,6,5,2,7,8] => 0101100 => 2

[[[[[]],[[],[],[]]]]] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,5,4,3,6,2,7,8] => 0110100 => 2

[[[[[]],[[],[[]]]]]] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,4,5,3,6,2,7,8] => 0010100 => 1

[[[[[]],[[[]],[]]]]] => [[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,3,5,4,6,2,7,8] => 0010100 => 1

[[[[[]],[[[],[]]]]]] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,4,3,5,6,2,7,8] => 0100100 => 1

[[[[[]],[[[[]]]]]]] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,3,4,5,6,2,7,8] => 0000100 => 1

[[[[[[]]],[],[],[]]]] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,2,6,5,4,3,7,8] => 0011100 => 3

[[[[[],[]],[],[[]]]]] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [2,1,5,6,4,3,7,8] => 1001100 => 2

[[[[[[]]],[],[[]]]]] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => 0001100 => 2

[[[[[],[]],[[]],[]]]] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [2,1,4,6,5,3,7,8] => 1001100 => 2

[[[[[[]]],[[]],[]]]] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,2,4,6,5,3,7,8] => 0001100 => 2

[[[[[[]]],[[[]]]]]] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,2,4,5,6,3,7,8] => 0000100 => 1

[[[[[],[],[]],[],[]]]] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [3,2,1,6,5,4,7,8] => 1101100 => 2

[[[[[],[[]]],[],[]]]] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [2,3,1,6,5,4,7,8] => 0101100 => 2

[[[[[[]],[]],[],[]]]] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,3,2,6,5,4,7,8] => 0101100 => 2

[[[[[[[]]]],[],[]]]] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,2,3,6,5,4,7,8] => 0001100 => 2

[[[[[],[],[]],[[]]]]] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [3,2,1,5,6,4,7,8] => 1100100 => 2

[[[[[],[[]]],[[]]]]] => [[[[.,[[.,.],.]],[[.,.],.]],.],.] => [2,3,1,5,6,4,7,8] => 0100100 => 1

[[[[[[]],[]],[[]]]]] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,3,2,5,6,4,7,8] => 0100100 => 1

[[[[[[[]]]],[[]]]]] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,2,3,5,6,4,7,8] => 0000100 => 1

[[[[[],[],[],[]],[]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => 1110100 => 3

[[[[[],[[]],[]],[]]]] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => 0110100 => 2

[[[[[],[[],[]]],[]]]] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => 1010100 => 1

[[[[[],[[[]]]],[]]]] => [[[[.,[[[.,.],.],.]],[.,.]],.],.] => [2,3,4,1,6,5,7,8] => 0010100 => 1

[[[[[[],[]],[]],[]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => 1010100 => 1

[[[[[[[]]],[]],[]]]] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => 0010100 => 1

[[[[[[[]],[]]],[]]]] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,3,2,4,6,5,7,8] => 0100100 => 1

[[[[[[[],[]]]],[]]]] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [2,1,3,4,6,5,7,8] => 1000100 => 1

[[[[[[[[]]]]],[]]]] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,2,3,4,6,5,7,8] => 0000100 => 1

[[[[[],[],[],[],[]]]]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 1111000 => 4

[[[[[],[],[],[[]]]]]] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => 0111000 => 3

[[[[[],[],[[]],[]]]]] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [3,5,4,2,1,6,7,8] => 0111000 => 3

[[[[[],[],[[],[]]]]]] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => 1011000 => 2

[[[[[],[],[[[]]]]]]] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => 0011000 => 2

[[[[[],[[]],[],[]]]]] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [2,5,4,3,1,6,7,8] => 0111000 => 3

[[[[[],[[]],[[]]]]]] => [[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => 0011000 => 2

[[[[[],[[],[]],[]]]]] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [3,2,5,4,1,6,7,8] => 1011000 => 2

[[[[[],[[[]]],[]]]]] => [[[[.,[[[.,.],.],[.,.]]],.],.],.] => [2,3,5,4,1,6,7,8] => 0011000 => 2

[[[[[],[[],[],[]]]]]] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => 1101000 => 2

[[[[[],[[],[[]]]]]]] => [[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => 0101000 => 1

[[[[[],[[[]],[]]]]]] => [[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => 0101000 => 1

[[[[[],[[[],[]]]]]]] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => 1001000 => 1

[[[[[],[[[[]]]]]]]] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 0001000 => 1

[[[[[[]],[],[],[]]]]] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8] => 0111000 => 3

[[[[[[]],[],[[]]]]]] => [[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,4,5,3,2,6,7,8] => 0011000 => 2

[[[[[[]],[[]],[]]]]] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,3,5,4,2,6,7,8] => 0011000 => 2

[[[[[[]],[[[]]]]]]] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,3,4,5,2,6,7,8] => 0001000 => 1

[[[[[[],[]],[],[]]]]] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8] => 1011000 => 2

[[[[[[[]]],[],[]]]]] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8] => 0011000 => 2

[[[[[[],[]],[[]]]]]] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [2,1,4,5,3,6,7,8] => 1001000 => 1

[[[[[[],[],[]],[]]]]] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8] => 1101000 => 2

[[[[[[],[[]]],[]]]]] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8] => 0101000 => 1

[[[[[[[]],[]],[]]]]] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => 0101000 => 1

[[[[[[[[]]]],[]]]]] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => 0001000 => 1

[[[[[[],[],[],[]]]]]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 1110000 => 3

[[[[[[],[],[[]]]]]]] => [[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => 0110000 => 2

[[[[[[],[[]],[]]]]]] => [[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => 0110000 => 2

[[[[[[],[[],[]]]]]]] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => 1010000 => 1

[[[[[[],[[[]]]]]]]] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => 0010000 => 1

[[[[[[[]],[],[]]]]]] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,4,3,2,5,6,7,8] => 0110000 => 2

[[[[[[[]],[[]]]]]]] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,3,4,2,5,6,7,8] => 0010000 => 1

[[[[[[[],[]],[]]]]]] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [2,1,4,3,5,6,7,8] => 1010000 => 1

[[[[[[[[]]],[]]]]]] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,2,4,3,5,6,7,8] => 0010000 => 1

[[[[[[[],[],[]]]]]]] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 1100000 => 2

[[[[[[[],[[]]]]]]]] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => 0100000 => 1

[[[[[[[[]],[]]]]]]] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => 0100000 => 1

[[[[[[[[],[]]]]]]]] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1000000 => 1

[[[[[[[[[]]]]]]]]] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0000000 => 0

[[],[[],[[],[[],[[],[]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => 101010101 => 1

[[],[[[[[],[]],[]],[]],[]]] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,10,1] => 101010101 => 1

[[[[[],[[],[]]],[]],[]],[]] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9] => 101010101 => 1

[[[[[[],[]],[]],[]],[]],[]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => 101010101 => 1

[[],[[[[[[],[]],[]],[]],[]],[]]] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,11,10,12,1] => 10101010101 => 1

[[[[[[[],[]],[]],[]],[]],[]],[]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => 10101010101 => 1

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Description

The length of the longest run of ones in a binary word.

Map

descent word

Description

The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.

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

to binary tree: right brother = right child

Description

Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.