- FindStat

Identifier

Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words

Images

[] => [] => [] =>

[[]] => [1,0] => [1] =>

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

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

[[],[],[]] => [1,0,1,0,1,0] => [1,2,3] => 11

[[],[[]]] => [1,0,1,1,0,0] => [1,3,2] => 10

[[[]],[]] => [1,1,0,0,1,0] => [2,1,3] => 01

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

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

[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 111

[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 110

[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 101

[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 100

[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 100

[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 011

[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 010

[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 001

[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 001

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

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

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

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

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

[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 1111

[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1110

[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 1101

[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1100

[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1100

[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 1011

[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1010

[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 1001

[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1001

[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000

[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000

[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000

[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000

[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000

[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 0111

[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 0110

[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 0101

[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100

[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100

[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 0011

[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0011

[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010

[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010

[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001

[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001

[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001

[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001

[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 11111

[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 11110

[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 11101

[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 11100

[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 11100

[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 11011

[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 11010

[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 11001

[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 11001

[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 11000

[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 11000

[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 11000

[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 11000

[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 11000

[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 10111

[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 10110

[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 10101

[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 10100

[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 10100

[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 10011

[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 10011

[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 10010

[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 10010

[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 10001

[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 10001

[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 10001

[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => 10001

[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 10001

[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 10000

[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 10000

[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 10000

[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 10000

[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 10000

[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 10000

[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 10000

[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 10000

>>> Load all 1419 entries. <<<

[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 10000

[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 10000

[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 10000

[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 10000

[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 10000

[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 10000

[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 01111

[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 01110

[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 01101

[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 01100

[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 01100

[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 01011

[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 01010

[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 01001

[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 01001

[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 01000

[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 01000

[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 01000

[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 01000

[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 01000

[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 00111

[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 00111

[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 00110

[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 00110

[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 00101

[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 00101

[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 00100

[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 00100

[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 00100

[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 00100

[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 00011

[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 00011

[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 00011

[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => 00011

[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 00011

[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 00010

[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 00010

[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 00010

[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => 00010

[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 00010

[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 00001

[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 00001

[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 00001

[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => 00001

[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 00001

[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 00001

[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 00001

[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => 00001

[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 00001

[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => 00001

[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => 00001

[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => 00001

[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 00001

[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 00001

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 111111

[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 111110

[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 111101

[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 111100

[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 111100

[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => 111011

[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => 111010

[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => 111001

[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => 111001

[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 111000

[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => 111000

[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 111000

[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => 111000

[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 111000

[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => 110111

[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => 110110

[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => 110101

[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => 110100

[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => 110100

[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => 110011

[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => 110011

[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => 110010

[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => 110010

[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => 110001

[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => 110001

[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => 110001

[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => 110001

[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 110001

[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 110000

[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => 110000

[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => 110000

[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => 110000

[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 110000

[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 110000

[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => 110000

[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => 110000

[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 110000

[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => 110000

[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => 110000

[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => 110000

[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => 110000

[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 110000

[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 101111

[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => 101110

[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => 101101

[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => 101100

[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => 101100

[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => 101011

[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => 101010

[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => 101001

[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => 101001

[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => 101000

[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => 101000

[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => 101000

[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => 101000

[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 101000

[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => 100111

[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => 100111

[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => 100110

[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => 100110

[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => 100101

[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => 100101

[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => 100100

[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => 100100

[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => 100100

[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 100100

[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => 100011

[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => 100011

[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => 100011

[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => 100011

[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => 100011

[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => 100010

[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => 100010

[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => 100010

[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => 100010

[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => 100010

[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => 100001

[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => 100001

[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => 100001

[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => 100001

[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 100001

[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => 100001

[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => 100001

[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => 100001

[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => 100001

[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => 100001

[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => 100001

[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => 100001

[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => 100001

[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => 100001

[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 100000

[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => 100000

[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => 100000

[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => 100000

[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 100000

[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => 100000

[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => 100000

[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => 100000

[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 100000

[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => 100000

[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => 100000

[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => 100000

[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => 100000

[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 100000

[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 100000

[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => 100000

[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => 100000

[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => 100000

[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 100000

[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => 100000

[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => 100000

[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => 100000

[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => 100000

[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => 100000

[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => 100000

[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => 100000

[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => 100000

[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => 100000

[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => 100000

[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => 100000

[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => 100000

[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => 100000

[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 100000

[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => 100000

[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => 100000

[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => 100000

[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => 100000

[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 100000

[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 100000

[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 100000

[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 100000

[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 100000

[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 011111

[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => 011110

[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => 011101

[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => 011100

[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => 011100

[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => 011011

[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => 011010

[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => 011001

[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => 011001

[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => 011000

[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => 011000

[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => 011000

[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => 011000

[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => 011000

[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => 010111

[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => 010110

[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => 010101

[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => 010100

[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => 010100

[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => 010011

[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => 010011

[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => 010010

[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => 010010

[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => 010001

[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => 010001

[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => 010001

[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => 010001

[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => 010001

[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => 010000

[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => 010000

[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => 010000

[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => 010000

[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => 010000

[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => 010000

[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => 010000

[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => 010000

[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => 010000

[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => 010000

[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => 010000

[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => 010000

[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => 010000

[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 010000

[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => 001111

[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => 001111

[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => 001110

[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => 001110

[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => 001101

[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => 001101

[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => 001100

[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => 001100

[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => 001100

[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => 001100

[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => 001011

[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => 001011

[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => 001010

[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => 001010

[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => 001001

[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => 001001

[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => 001001

[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => 001001

[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => 001000

[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => 001000

[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => 001000

[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => 001000

[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => 001000

[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => 001000

[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => 001000

[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => 001000

[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => 001000

[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => 001000

[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => 000111

[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => 000111

[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => 000111

[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => 000111

[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => 000111

[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => 000110

[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => 000110

[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => 000110

[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => 000110

[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => 000110

[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => 000101

[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => 000101

[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => 000101

[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => 000101

[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => 000101

[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => 000100

[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => 000100

[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => 000100

[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => 000100

[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => 000100

[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => 000100

[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => 000100

[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => 000100

[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => 000100

[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => 000100

[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => 000011

[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => 000011

[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => 000011

[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => 000011

[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => 000011

[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => 000011

[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => 000011

[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => 000011

[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => 000011

[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => 000011

[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => 000011

[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => 000011

[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => 000011

[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => 000011

[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => 000010

[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => 000010

[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => 000010

[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => 000010

[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => 000010

[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => 000010

[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => 000010

[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => 000010

[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => 000010

[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => 000010

[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => 000010

[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => 000010

[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => 000010

[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 000010

[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => 000001

[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => 000001

[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => 000001

[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => 000001

[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => 000001

[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => 000001

[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => 000001

[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => 000001

[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => 000001

[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => 000001

[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => 000001

[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => 000001

[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => 000001

[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => 000001

[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => 000001

[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => 000001

[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => 000001

[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => 000001

[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => 000001

[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => 000001

[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => 000001

[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => 000001

[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => 000001

[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => 000001

[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => 000001

[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => 000001

[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => 000001

[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 000001

[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => 000001

[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => 000001

[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => 000001

[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => 000001

[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => 000001

[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => 000001

[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => 000001

[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => 000001

[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => 000001

[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => 000001

[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => 000001

[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => 000001

[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => 000001

[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 000001

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[],[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 1111111

[[],[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1111110

[[],[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 1111101

[[],[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => 1111100

[[],[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => 1111100

[[],[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => 1111011

[[],[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => 1111010

[[],[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => 1111001

[[],[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => 1111001

[[],[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => 1111000

[[],[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => 1111000

[[],[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => 1111000

[[],[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => 1111000

[[],[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => 1111000

[[],[],[],[[]],[],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => 1110111

[[],[],[],[[]],[],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => 1110110

[[],[],[],[[]],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 1110101

[[],[],[],[[]],[[],[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => 1110100

[[],[],[],[[]],[[[]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => 1110100

[[],[],[],[[],[]],[],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => 1110011

[[],[],[],[[[]]],[],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => 1110011

[[],[],[],[[],[]],[[]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => 1110010

[[],[],[],[[[]]],[[]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => 1110010

[[],[],[],[[],[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => 1110001

[[],[],[],[[],[[]]],[]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => 1110001

[[],[],[],[[[]],[]],[]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => 1110001

[[],[],[],[[[],[]]],[]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => 1110001

[[],[],[],[[[[]]]],[]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => 1110001

[[],[],[],[[],[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 1110000

[[],[],[],[[],[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => 1110000

[[],[],[],[[],[[]],[]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => 1110000

[[],[],[],[[],[[],[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => 1110000

[[],[],[],[[],[[[]]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => 1110000

[[],[],[],[[[]],[],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => 1110000

[[],[],[],[[[]],[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => 1110000

[[],[],[],[[[],[]],[]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => 1110000

[[],[],[],[[[[]]],[]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => 1110000

[[],[],[],[[[],[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => 1110000

[[],[],[],[[[],[[]]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => 1110000

[[],[],[],[[[[]],[]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => 1110000

[[],[],[],[[[[],[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => 1110000

[[],[],[],[[[[[]]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => 1110000

[[],[],[[]],[],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => 1101111

[[],[],[[]],[],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => 1101110

[[],[],[[]],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => 1101101

[[],[],[[]],[],[[],[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => 1101100

[[],[],[[]],[],[[[]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => 1101100

[[],[],[[]],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 1101011

[[],[],[[]],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => 1101010

[[],[],[[]],[[],[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => 1101001

[[],[],[[]],[[],[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => 1101000

[[],[],[[]],[[],[[]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => 1101000

[[],[],[[]],[[[],[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => 1101000

[[],[],[[]],[[[[]]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => 1101000

[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => 1100111

[[],[],[[[]]],[],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => 1100110

[[],[],[[],[]],[[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => 1100101

[[],[],[[],[]],[[],[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => 1100100

[[],[],[[],[]],[[[]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => 1100100

[[],[],[[[]]],[[],[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => 1100100

[[],[],[[[]]],[[[]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => 1100100

[[],[],[[],[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => 1100011

[[],[],[[[],[]]],[],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => 1100011

[[],[],[[[[]]]],[],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => 1100011

[[],[],[[],[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => 1100010

[[],[],[[],[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => 1100001

[[],[],[[[]],[],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => 1100001

[[],[],[[[[]],[]]],[]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => 1100001

[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => 1100001

[[],[],[[],[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => 1100000

[[],[],[[],[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => 1100000

[[],[],[[],[],[[],[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => 1100000

[[],[],[[],[],[[[]]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => 1100000

[[],[],[[],[[]],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => 1100000

[[],[],[[],[[],[]],[]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => 1100000

[[],[],[[],[[[]]],[]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => 1100000

[[],[],[[],[[[]],[]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => 1100000

[[],[],[[],[[[[]]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => 1100000

[[],[],[[[]],[],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => 1100000

[[],[],[[[]],[],[[]]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => 1100000

[[],[],[[[]],[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => 1100000

[[],[],[[[]],[[],[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => 1100000

[[],[],[[[]],[[[]]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => 1100000

[[],[],[[[],[]],[],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => 1100000

[[],[],[[[[]]],[],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => 1100000

[[],[],[[[[]]],[[]]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => 1100000

[[],[],[[[],[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => 1100000

[[],[],[[[[]],[]],[]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => 1100000

[[],[],[[[],[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => 1100000

[[],[],[[[],[[[]]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => 1100000

[[],[],[[[[]],[],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => 1100000

[[],[],[[[[]],[[]]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => 1100000

[[],[],[[[[[]]],[]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => 1100000

[[],[],[[[[[]],[]]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => 1100000

[[],[],[[[[[],[]]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => 1100000

[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => 1100000

[[],[[]],[],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => 1011111

[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => 1011110

[[],[[]],[],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 1011101

[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => 1011100

[[],[[]],[],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => 1011100

[[],[[]],[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => 1011011

[[],[[]],[],[[]],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => 1011010

[[],[[]],[],[[[]]],[]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => 1011001

[[],[[]],[],[[],[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => 1011000

[[],[[]],[],[[],[[]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => 1011000

[[],[[]],[],[[[],[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => 1011000

[[],[[]],[],[[[[]]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => 1011000

[[],[[]],[[]],[],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 1010111

[[],[[]],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1010101

[[],[[]],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => 1010100

[[],[[]],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => 1010100

[[],[[]],[[[]]],[],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => 1010011

[[],[[]],[[],[]],[[]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => 1010010

[[],[[]],[[[]]],[[]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => 1010010

[[],[[]],[[],[[]]],[]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => 1010001

[[],[[]],[[[]],[]],[]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => 1010001

[[],[[]],[[],[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => 1010000

[[],[[]],[[],[[[]]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => 1010000

[[],[[]],[[[]],[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => 1010000

[[],[[]],[[[],[]],[]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => 1010000

[[],[[]],[[[[]]],[]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => 1010000

[[],[[]],[[[],[[]]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => 1010000

[[],[[]],[[[[]],[]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => 1010000

[[],[[]],[[[[],[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => 1010000

[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => 1010000

[[],[[],[]],[],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => 1001111

[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => 1001111

[[],[[],[]],[],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => 1001110

[[],[[[]]],[],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => 1001110

[[],[[[]]],[],[[]],[]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => 1001101

[[],[[],[]],[],[[],[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => 1001100

[[],[[[]]],[],[[],[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => 1001100

[[],[[[]]],[],[[[]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => 1001100

[[],[[],[]],[[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => 1001010

[[],[[],[]],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => 1001001

[[],[[[]]],[[],[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => 1001001

[[],[[[]]],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1001001

[[],[[],[]],[[],[[]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => 1001000

[[],[[],[]],[[[],[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => 1001000

[[],[[],[]],[[[[]]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => 1001000

[[],[[[]]],[[],[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => 1001000

[[],[[[]]],[[],[[]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => 1001000

[[],[[[]]],[[[]],[]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => 1001000

[[],[[[]]],[[[],[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => 1001000

[[],[[[]]],[[[[]]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => 1001000

[[],[[],[],[]],[],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => 1000111

[[],[[[],[]]],[],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => 1000111

[[],[[],[[]]],[],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => 1000110

[[],[[],[],[]],[[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => 1000101

[[],[[],[[]]],[[]],[]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => 1000101

[[],[[[]],[]],[[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => 1000101

[[],[[],[],[]],[[],[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => 1000100

[[],[[],[],[]],[[[]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => 1000100

[[],[[],[[]]],[[],[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => 1000100

[[],[[[],[]]],[[],[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => 1000100

[[],[[[],[]]],[[[]]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => 1000100

[[],[[[[]]]],[[],[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => 1000100

[[],[[[[]]]],[[[]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => 1000100

[[],[[],[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => 1000011

[[],[[[]],[],[]],[],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => 1000011

[[],[[[]],[[]]],[],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => 1000011

[[],[[[[]]],[]],[],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => 1000011

[[],[[[],[],[]]],[],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => 1000011

[[],[[[],[[]]]],[],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => 1000011

[[],[[[[]],[]]],[],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => 1000011

[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => 1000011

[[],[[],[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => 1000010

[[],[[],[[],[]]],[[]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => 1000010

[[],[[],[[[]]]],[[]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => 1000010

[[],[[[],[]],[]],[[]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => 1000010

[[],[[[[],[]]]],[[]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => 1000010

[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => 1000010

[[],[[],[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => 1000001

[[],[[],[[]],[[]]],[]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => 1000001

[[],[[],[[],[]],[]],[]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => 1000001

[[],[[],[[[]]],[]],[]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => 1000001

[[],[[[]],[],[[]]],[]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => 1000001

[[],[[[]],[[]],[]],[]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => 1000001

[[],[[[],[]],[],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => 1000001

[[],[[[],[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => 1000001

[[],[[[],[[]],[]]],[]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => 1000001

[[],[[[],[[[]]]]],[]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => 1000001

[[],[[[[[]]],[]]],[]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => 1000001

[[],[[[[],[[]]]]],[]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => 1000001

[[],[[[[[],[]]]]],[]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => 1000001

[[],[[[[[[]]]]]],[]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => 1000001

[[],[[],[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => 1000000

[[],[[],[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => 1000000

[[],[[],[],[[]],[],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => 1000000

[[],[[],[],[[[]]],[]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => 1000000

[[],[[],[],[[[[]]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => 1000000

[[],[[],[[]],[[[]]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => 1000000

[[],[[],[[],[]],[],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => 1000000

[[],[[],[[],[]],[[]]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => 1000000

[[],[[],[[[]]],[[]]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => 1000000

[[],[[],[[],[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => 1000000

[[],[[],[[],[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => 1000000

[[],[[],[[],[[],[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => 1000000

[[],[[],[[[]],[],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => 1000000

[[],[[],[[[]],[[]]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => 1000000

[[],[[],[[[],[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => 1000000

[[],[[],[[[],[[]]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => 1000000

[[],[[],[[[[]],[]]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => 1000000

[[],[[],[[[[],[]]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => 1000000

[[],[[],[[[[[]]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => 1000000

[[],[[[]],[],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => 1000000

[[],[[[]],[],[[],[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => 1000000

[[],[[[]],[],[[[]]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => 1000000

[[],[[[]],[[]],[],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => 1000000

[[],[[[]],[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => 1000000

[[],[[[]],[[],[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => 1000000

[[],[[[]],[[],[[]]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => 1000000

[[],[[[]],[[[]],[]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => 1000000

[[],[[[]],[[[],[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => 1000000

[[],[[[]],[[[[]]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => 1000000

[[],[[[],[]],[],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => 1000000

[[],[[[[]]],[],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => 1000000

[[],[[[[]]],[],[[]]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => 1000000

[[],[[[],[]],[[],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => 1000000

[[],[[[],[],[]],[[]]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => 1000000

[[],[[[],[[]]],[[]]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => 1000000

[[],[[[[]],[]],[[]]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => 1000000

[[],[[[[],[]]],[[]]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => 1000000

[[],[[[[[]]]],[[]]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => 1000000

[[],[[[],[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => 1000000

[[],[[[[[]]],[]],[]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => 1000000

[[],[[[[],[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => 1000000

[[],[[[[[[]]]]],[]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => 1000000

[[],[[[],[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => 1000000

[[],[[[],[],[[],[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => 1000000

[[],[[[],[],[[[]]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => 1000000

[[],[[[],[[]],[],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => 1000000

[[],[[[],[[],[]],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => 1000000

[[],[[[],[[[]]],[]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => 1000000

[[],[[[],[[],[[]]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => 1000000

[[],[[[],[[[],[]]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => 1000000

[[],[[[],[[[[]]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => 1000000

[[],[[[[]],[],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => 1000000

[[],[[[[]],[],[[]]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => 1000000

[[],[[[[]],[[]],[]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => 1000000

[[],[[[[]],[[],[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => 1000000

[[],[[[[],[]],[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => 1000000

[[],[[[[[]]],[],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => 1000000

[[],[[[[],[[]]],[]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => 1000000

[[],[[[[[]],[]],[]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => 1000000

[[],[[[[[],[]]],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => 1000000

[[],[[[[[[]]]],[]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => 1000000

[[],[[[[],[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => 1000000

[[],[[[[],[[]],[]]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => 1000000

[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => 1000000

[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => 1000000

[[],[[[[[]],[[]]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => 1000000

[[],[[[[[],[]],[]]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => 1000000

[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => 1000000

[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => 1000000

[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 1000000

[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => 1000000

[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 1000000

[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 1000000

[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => 0111111

[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 0111110

[[[]],[],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => 0111101

[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => 0111100

[[[]],[],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => 0111100

[[[]],[],[],[[]],[],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => 0111011

[[[]],[],[],[[]],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => 0111010

[[[]],[],[],[[],[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => 0111000

[[[]],[],[],[[[],[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => 0111000

[[[]],[],[],[[[[]]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => 0111000

[[[]],[],[[]],[],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => 0110111

[[[]],[],[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => 0110110

[[[]],[],[[]],[[],[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => 0110100

[[[]],[],[[]],[[[]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => 0110100

[[[]],[],[[],[]],[[]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => 0110010

[[[]],[],[[[]]],[[]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => 0110010

[[[]],[],[[],[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => 0110000

[[[]],[],[[[]],[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => 0110000

[[[]],[],[[[],[[]]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => 0110000

[[[]],[],[[[[]],[]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => 0110000

[[[]],[],[[[[],[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => 0110000

[[[]],[],[[[[[]]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => 0110000

[[[]],[[]],[],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => 0101111

[[[]],[[]],[],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => 0101110

[[[]],[[]],[],[[],[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => 0101100

[[[]],[[]],[],[[[]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => 0101100

[[[]],[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => 0101011

[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 0101010

[[[]],[[]],[[],[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => 0101001

[[[]],[[]],[[],[[]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => 0101000

[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 0101000

[[[]],[[],[]],[],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => 0100111

[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => 0100111

[[[]],[[[]]],[],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => 0100110

[[[]],[[[]]],[[]],[]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => 0100101

[[[]],[[],[]],[[[]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => 0100100

[[[]],[[[]]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => 0100100

[[[]],[[],[[]]],[],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => 0100011

[[[]],[[],[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => 0100010

[[[]],[[[]],[]],[[]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => 0100010

[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => 0100010

[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 0100010

[[[]],[[],[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => 0100001

[[[]],[[[]],[],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => 0100001

[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => 0100001

[[[]],[[],[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => 0100000

[[[]],[[],[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => 0100000

[[[]],[[],[],[[],[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => 0100000

[[[]],[[],[],[[[]]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => 0100000

[[[]],[[],[[]],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => 0100000

[[[]],[[],[[[]]],[]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => 0100000

[[[]],[[],[[[]],[]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => 0100000

[[[]],[[],[[[[]]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => 0100000

[[[]],[[[]],[],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => 0100000

[[[]],[[[]],[],[[]]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => 0100000

[[[]],[[[]],[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => 0100000

[[[]],[[[]],[[[]]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => 0100000

[[[]],[[[],[]],[[]]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => 0100000

[[[]],[[[[],[]]],[]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => 0100000

[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => 0100000

[[[]],[[[],[],[[]]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => 0100000

[[[]],[[[],[[],[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => 0100000

[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => 0100000

[[[]],[[[[]],[],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => 0100000

[[[]],[[[[]],[[]]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => 0100000

[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => 0100000

[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => 0100000

[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => 0100000

[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => 0100000

[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => 0100000

[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 0100000

[[[],[]],[],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => 0011111

[[[[]]],[],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => 0011111

[[[],[]],[],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => 0011110

[[[[]]],[],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => 0011110

[[[],[]],[],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => 0011101

[[[[]]],[],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => 0011101

[[[],[]],[],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => 0011100

[[[[]]],[],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => 0011100

[[[[]]],[],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => 0011100

[[[],[]],[],[[]],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => 0011010

[[[[]]],[],[[[]]],[]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => 0011001

[[[],[]],[],[[],[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => 0011000

[[[],[]],[],[[[[]]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => 0011000

[[[[]]],[],[[],[[]]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => 0011000

[[[[]]],[],[[[],[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => 0011000

[[[[]]],[],[[[[]]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => 0011000

[[[],[]],[[]],[],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => 0010111

[[[[]]],[[]],[],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => 0010111

[[[],[]],[[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => 0010101

[[[[]]],[[]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => 0010101

[[[],[]],[[],[]],[],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => 0010011

[[[],[]],[[[]]],[],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => 0010011

[[[[]]],[[],[]],[],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => 0010011

[[[[]]],[[[]]],[],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => 0010011

[[[],[]],[[[]]],[[]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => 0010010

[[[[]]],[[[]]],[[]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => 0010010

[[[],[]],[[],[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => 0010001

[[[],[]],[[[]],[]],[]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => 0010001

[[[[]]],[[],[[]]],[]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => 0010001

[[[[]]],[[[]],[]],[]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => 0010001

[[[[]]],[[[],[]]],[]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => 0010001

[[[[]]],[[[[]]]],[]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => 0010001

[[[],[]],[[],[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => 0010000

[[[],[]],[[[]],[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => 0010000

[[[],[]],[[[],[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => 0010000

[[[],[]],[[[[],[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => 0010000

[[[],[]],[[[[[]]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => 0010000

[[[[]]],[[],[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => 0010000

[[[[]]],[[],[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => 0010000

[[[[]]],[[],[[]],[]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => 0010000

[[[[]]],[[],[[],[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => 0010000

[[[[]]],[[],[[[]]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => 0010000

[[[[]]],[[[]],[],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => 0010000

[[[[]]],[[[]],[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => 0010000

[[[[]]],[[[],[]],[]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => 0010000

[[[[]]],[[[[]]],[]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => 0010000

[[[[]]],[[[],[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => 0010000

[[[[]]],[[[],[[]]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => 0010000

[[[[]]],[[[[]],[]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => 0010000

[[[[]]],[[[[],[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => 0010000

[[[[]]],[[[[[]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 0010000

[[[],[],[]],[],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => 0001111

[[[],[[]]],[],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => 0001111

[[[[]],[]],[],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => 0001111

[[[[],[]]],[],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => 0001111

[[[[[]]]],[],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => 0001111

[[[],[],[]],[],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => 0001110

[[[[[]]]],[],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => 0001110

[[[[],[]]],[],[[]],[]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => 0001101

[[[[[]]]],[],[[]],[]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => 0001101

[[[],[[]]],[],[[[]]]] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => 0001100

[[[[]],[]],[],[[[]]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => 0001100

[[[[],[]]],[],[[[]]]] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => 0001100

[[[[[]]]],[],[[],[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => 0001100

[[[[[]]]],[],[[[]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => 0001100

[[[],[],[]],[[]],[],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => 0001011

[[[],[[]]],[[]],[],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => 0001011

[[[[]],[]],[[]],[],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => 0001011

[[[[],[]]],[[]],[],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => 0001011

[[[[[]]]],[[]],[],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => 0001011

[[[],[],[]],[[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => 0001010

[[[[]],[]],[[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => 0001010

[[[[[]]]],[[]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 0001010

[[[],[],[]],[[],[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => 0001001

[[[],[],[]],[[[]]],[]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => 0001001

[[[[],[]]],[[[]]],[]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => 0001001

[[[[[]]]],[[],[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => 0001001

[[[[[]]]],[[[]]],[]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => 0001001

[[[],[],[]],[[],[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => 0001000

[[[],[],[]],[[[[]]]]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => 0001000

[[[],[[]]],[[[]],[]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => 0001000

[[[],[[]]],[[[[]]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => 0001000

[[[[]],[]],[[],[[]]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => 0001000

[[[[]],[]],[[[]],[]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => 0001000

[[[[]],[]],[[[],[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => 0001000

[[[[]],[]],[[[[]]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => 0001000

[[[[],[]]],[[[],[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => 0001000

[[[[],[]]],[[[[]]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => 0001000

[[[[[]]]],[[],[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => 0001000

[[[[[]]]],[[],[[]]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => 0001000

[[[[[]]]],[[[]],[]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => 0001000

[[[[[]]]],[[[],[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => 0001000

[[[[[]]]],[[[[]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 0001000

[[[],[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => 0000111

[[[],[],[[]]],[],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => 0000111

[[[],[[]],[]],[],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => 0000111

[[[],[[],[]]],[],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => 0000111

[[[],[[[]]]],[],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => 0000111

[[[[]],[],[]],[],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => 0000111

[[[[]],[[]]],[],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => 0000111

[[[[],[]],[]],[],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => 0000111

[[[[[]]],[]],[],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => 0000111

[[[[],[],[]]],[],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => 0000111

[[[[],[[]]]],[],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => 0000111

[[[[[]],[]]],[],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => 0000111

[[[[[],[]]]],[],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => 0000111

[[[[[[]]]]],[],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => 0000111

[[[],[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => 0000110

[[[],[],[[]]],[],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => 0000110

[[[],[[]],[]],[],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => 0000110

[[[],[[[]]]],[],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => 0000110

[[[[]],[[]]],[],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => 0000110

[[[[],[]],[]],[],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => 0000110

[[[[],[[]]]],[],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => 0000110

[[[[[]],[]]],[],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => 0000110

[[[[[],[]]]],[],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => 0000110

[[[[[[]]]]],[],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => 0000110

[[[],[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => 0000101

[[[],[],[[]]],[[]],[]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => 0000101

[[[],[[]],[]],[[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => 0000101

[[[[]],[[]]],[[]],[]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => 0000101

[[[[],[[]]]],[[]],[]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => 0000101

[[[[[]],[]]],[[]],[]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => 0000101

[[[[[[]]]]],[[]],[]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => 0000101

[[[],[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => 0000100

[[[],[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => 0000100

[[[],[],[[]]],[[[]]]] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => 0000100

[[[],[[]],[]],[[[]]]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => 0000100

[[[],[[],[]]],[[[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => 0000100

[[[],[[[]]]],[[[]]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => 0000100

[[[[]],[],[]],[[[]]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => 0000100

[[[[]],[[]]],[[],[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => 0000100

[[[[]],[[]]],[[[]]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => 0000100

[[[[],[]],[]],[[],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => 0000100

[[[[],[]],[]],[[[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => 0000100

[[[[[]]],[]],[[[]]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => 0000100

[[[[],[],[]]],[[],[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => 0000100

[[[[],[],[]]],[[[]]]] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => 0000100

[[[[],[[]]]],[[[]]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => 0000100

[[[[[]],[]]],[[[]]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => 0000100

[[[[[],[]]]],[[],[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => 0000100

[[[[[],[]]]],[[[]]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => 0000100

[[[[[[]]]]],[[],[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => 0000100

[[[[[[]]]]],[[[]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 0000100

[[[],[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => 0000011

[[[],[],[],[[]]],[],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => 0000011

[[[],[],[[]],[]],[],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => 0000011

[[[],[[]],[[]]],[],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => 0000011

[[[],[[[],[]]]],[],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => 0000011

[[[[]],[],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => 0000011

[[[[],[]],[],[]],[],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => 0000011

[[[[[]]],[],[]],[],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => 0000011

[[[[[]]],[[]]],[],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => 0000011

[[[[],[],[]],[]],[],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => 0000011

[[[[],[[]]],[]],[],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => 0000011

[[[[[]],[]],[]],[],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => 0000011

[[[[[[]]]],[]],[],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => 0000011

[[[[],[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => 0000011

[[[[],[],[[]]]],[],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => 0000011

[[[[],[[],[]]]],[],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => 0000011

[[[[],[[[]]]]],[],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => 0000011

[[[[[]],[[]]]],[],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => 0000011

[[[[[[]]],[]]],[],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => 0000011

[[[[[[],[]]]]],[],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => 0000011

[[[[[[[]]]]]],[],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => 0000011

[[[],[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => 0000010

[[[],[[]],[],[]],[[]]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => 0000010

[[[],[[],[[]]]],[[]]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => 0000010

[[[],[[[[]]]]],[[]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => 0000010

[[[[]],[[]],[]],[[]]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => 0000010

[[[[],[]],[],[]],[[]]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => 0000010

[[[[[]]],[],[]],[[]]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => 0000010

[[[[[]]],[[]]],[[]]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => 0000010

[[[[],[],[]],[]],[[]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => 0000010

[[[[],[[]]],[]],[[]]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => 0000010

[[[[[]],[]],[]],[[]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => 0000010

[[[[[[]]]],[]],[[]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => 0000010

[[[[],[],[[]]]],[[]]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => 0000010

[[[[],[[[]]]]],[[]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => 0000010

[[[[[]],[[]]]],[[]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => 0000010

[[[[[[]]],[]]],[[]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => 0000010

[[[[[],[],[]]]],[[]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => 0000010

[[[[[],[[]]]]],[[]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => 0000010

[[[[[[]],[]]]],[[]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => 0000010

[[[[[[],[]]]]],[[]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => 0000010

[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 0000010

[[[],[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => 0000001

[[[],[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => 0000001

[[[],[],[],[[]],[]],[]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => 0000001

[[[],[],[],[[[]]]],[]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => 0000001

[[[],[],[[[],[]]]],[]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => 0000001

[[[],[],[[[[]]]]],[]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => 0000001

[[[],[[]],[[]],[]],[]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => 0000001

[[[],[[],[]],[],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => 0000001

[[[],[[[]]],[],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => 0000001

[[[],[[],[[[]]]]],[]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => 0000001

[[[],[[[],[[]]]]],[]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => 0000001

[[[],[[[[[]]]]]],[]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => 0000001

[[[[]],[],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => 0000001

[[[[]],[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => 0000001

[[[[]],[[[]]],[]],[]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => 0000001

[[[[]],[[],[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => 0000001

[[[[]],[[],[[]]]],[]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => 0000001

[[[[]],[[[]],[]]],[]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => 0000001

[[[[]],[[[],[]]]],[]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => 0000001

[[[[]],[[[[]]]]],[]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => 0000001

[[[[],[]],[],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => 0000001

[[[[[]]],[],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => 0000001

[[[[[]]],[[]],[]],[]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => 0000001

[[[[],[]],[[],[]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => 0000001

[[[[],[],[]],[],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => 0000001

[[[[],[[]]],[],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => 0000001

[[[[[[]]]],[],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => 0000001

[[[[],[],[]],[[]]],[]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => 0000001

[[[[],[[]]],[[]]],[]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => 0000001

[[[[[]],[]],[[]]],[]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => 0000001

[[[[[],[]]],[[]]],[]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => 0000001

[[[[[[]]]],[[]]],[]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => 0000001

[[[[],[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => 0000001

[[[[],[],[[]]],[]],[]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => 0000001

[[[[[]],[],[]],[]],[]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => 0000001

[[[[[]],[[]]],[]],[]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => 0000001

[[[[[],[],[]]],[]],[]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => 0000001

[[[[[],[[]]]],[]],[]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => 0000001

[[[[[[[]]]]],[]],[]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => 0000001

[[[[],[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => 0000001

[[[[],[],[],[[]]]],[]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => 0000001

[[[[],[],[[]],[]]],[]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => 0000001

[[[[],[],[[],[]]]],[]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => 0000001

[[[[],[],[[[]]]]],[]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => 0000001

[[[[],[[]],[[]]]],[]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => 0000001

[[[[],[[],[]],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => 0000001

[[[[],[[[]]],[]]],[]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => 0000001

[[[[],[[],[[]]]]],[]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => 0000001

[[[[],[[[],[]]]]],[]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => 0000001

[[[[[]],[[]],[]]],[]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => 0000001

[[[[[],[]],[[]]]],[]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => 0000001

[[[[[],[[]]],[]]],[]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => 0000001

[[[[[[]],[]],[]]],[]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => 0000001

[[[[[[],[]]],[]]],[]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => 0000001

[[[[[[[]]]],[]]],[]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => 0000001

[[[[[],[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => 0000001

[[[[[],[],[[]]]]],[]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => 0000001

[[[[[],[[]],[]]]],[]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => 0000001

[[[[[],[[],[]]]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => 0000001

[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => 0000001

[[[[[[]],[[]]]]],[]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => 0000001

[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => 0000001

[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => 0000001

[[[[[[],[[]]]]]],[]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => 0000001

[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => 0000001

[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => 0000001

[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 0000001

[[[],[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 0000000

[[[],[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => 0000000

[[[],[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => 0000000

[[[],[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => 0000000

[[[],[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => 0000000

[[[],[],[],[[]],[],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => 0000000

[[[],[],[],[[]],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => 0000000

[[[],[],[],[[[]]],[]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => 0000000

[[[],[],[],[[],[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => 0000000

[[[],[],[],[[[]],[]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => 0000000

[[[],[],[],[[[],[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => 0000000

[[[],[],[],[[[[]]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => 0000000

[[[],[],[[]],[],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => 0000000

[[[],[],[[]],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => 0000000

[[[],[],[[]],[[[]]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => 0000000

[[[],[],[[],[]],[],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => 0000000

[[[],[],[[[]]],[],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => 0000000

[[[],[],[[],[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => 0000000

[[[],[],[[],[[]]],[]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => 0000000

[[[],[],[[[]],[]],[]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => 0000000

[[[],[],[[[],[]]],[]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => 0000000

[[[],[],[[[[]]]],[]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => 0000000

[[[],[],[[],[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => 0000000

[[[],[],[[[]],[],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => 0000000

[[[],[],[[[],[]],[]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => 0000000

[[[],[],[[[[]]],[]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => 0000000

[[[],[],[[[[[]]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => 0000000

[[[],[[]],[],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => 0000000

[[[],[[]],[],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => 0000000

[[[],[[]],[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => 0000000

[[[],[[]],[],[[],[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => 0000000

[[[],[[]],[[]],[],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => 0000000

[[[],[[]],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => 0000000

[[[],[[]],[[[]]],[]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => 0000000

[[[],[[]],[[[[]]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => 0000000

[[[],[[],[]],[],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => 0000000

[[[],[[[]]],[],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => 0000000

[[[],[[[]]],[],[[]]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => 0000000

[[[],[[[]]],[[]],[]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => 0000000

[[[],[[],[]],[[],[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => 0000000

[[[],[[],[]],[[[]]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => 0000000

[[[],[[[]]],[[],[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => 0000000

[[[],[[[]]],[[[]]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => 0000000

[[[],[[],[],[]],[],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => 0000000

[[[],[[],[[]]],[],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,6,3,5,4,7,8,1] => 0000000

[[[],[[[]],[]],[],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => 0000000

[[[],[[[],[]]],[],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => 0000000

[[[],[[[[]]]],[],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => 0000000

[[[],[[[[]]]],[[]]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => 0000000

[[[],[[],[[]],[]],[]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => 0000000

[[[],[[],[[],[]]],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => 0000000

[[[],[[[]],[],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => 0000000

[[[],[[[[]]],[]],[]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => 0000000

[[[],[[[[]],[]]],[]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => 0000000

[[[],[[[[[]]]]],[]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => 0000000

[[[],[[],[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => 0000000

[[[],[[],[[],[[]]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => 0000000

[[[],[[],[[[[]]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => 0000000

[[[],[[[]],[],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => 0000000

[[[],[[[]],[],[[]]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => 0000000

[[[],[[[]],[[],[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => 0000000

[[[],[[[]],[[[]]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => 0000000

[[[],[[[],[]],[],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => 0000000

[[[],[[[[]]],[],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => 0000000

[[[],[[[[]],[],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => 0000000

[[[],[[[[]],[[]]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => 0000000

[[[],[[[[],[[]]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => 0000000

[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => 0000000

[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => 0000000

[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => 0000000

[[[[]],[],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => 0000000

[[[[]],[],[],[[]],[]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => 0000000

[[[[]],[],[],[[],[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => 0000000

[[[[]],[],[[[]]],[]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => 0000000

[[[[]],[],[[[],[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => 0000000

[[[[]],[],[[[[]]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => 0000000

[[[[]],[[]],[],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => 0000000

[[[[]],[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => 0000000

[[[[]],[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => 0000000

[[[[]],[[[]]],[[]]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => 0000000

[[[[]],[[],[[]]],[]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => 0000000

[[[[]],[[[],[]]],[]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => 0000000

[[[[]],[[[[]]]],[]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => 0000000

[[[[]],[[],[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => 0000000

[[[[]],[[[]],[],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => 0000000

[[[[]],[[[]],[[]]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => 0000000

[[[[]],[[[],[[]]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => 0000000

[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => 0000000

[[[[],[]],[],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => 0000000

[[[[[]]],[],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => 0000000

[[[[],[]],[],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => 0000000

[[[[[]]],[],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => 0000000

[[[[[]]],[],[[]],[]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => 0000000

[[[[[]]],[],[[[]]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => 0000000

[[[[[]]],[[]],[],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => 0000000

[[[[],[]],[[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => 0000000

[[[[[]]],[[]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => 0000000

[[[[],[]],[[],[]],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => 0000000

[[[[],[]],[[[]]],[]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => 0000000

[[[[[]]],[[],[]],[]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => 0000000

[[[[[]]],[[[]]],[]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => 0000000

[[[[],[]],[[],[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => 0000000

[[[[],[]],[[[[]]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => 0000000

[[[[[]]],[[],[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => 0000000

[[[[[]]],[[],[[]]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => 0000000

[[[[[]]],[[[],[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => 0000000

[[[[[]]],[[[[]]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => 0000000

[[[[],[],[]],[],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => 0000000

[[[[[]],[]],[],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => 0000000

[[[[[],[]]],[],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => 0000000

[[[[[[]]]],[],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => 0000000

[[[[[[]]]],[],[[]]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => 0000000

[[[[],[[]]],[[]],[]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => 0000000

[[[[[[]]]],[[]],[]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => 0000000

[[[[],[],[]],[[[]]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => 0000000

[[[[[[]]]],[[],[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => 0000000

[[[[[[]]]],[[[]]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => 0000000

[[[[],[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => 0000000

[[[[[]],[[]]],[],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => 0000000

[[[[[],[],[]]],[],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => 0000000

[[[[[[[]]]]],[],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => 0000000

[[[[[],[],[]]],[[]]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => 0000000

[[[[[[[]]]]],[[]]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => 0000000

[[[[],[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => 0000000

[[[[],[[]],[[]]],[]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => 0000000

[[[[],[[],[]],[]],[]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => 0000000

[[[[[[]]],[],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => 0000000

[[[[[],[]],[[]]],[]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => 0000000

[[[[[[]]],[[]]],[]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => 0000000

[[[[[[]],[]],[]],[]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => 0000000

[[[[[[[]]]],[]],[]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => 0000000

[[[[[],[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => 0000000

[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => 0000000

[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => 0000000

[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => 0000000

[[[[[[],[],[]]]],[]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => 0000000

[[[[[[],[[]]]]],[]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => 0000000

[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => 0000000

[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => 0000000

[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => 0000000

[[[[],[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => 0000000

[[[[],[],[[]],[],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => 0000000

[[[[],[],[[[]]],[]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => 0000000

[[[[],[],[[[],[]]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => 0000000

[[[[],[[]],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => 0000000

[[[[],[[]],[[],[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => 0000000

[[[[],[[[]]],[],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => 0000000

[[[[],[[],[]],[[]]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => 0000000

[[[[],[[[]]],[[]]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => 0000000

[[[[],[[[],[]]],[]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => 0000000

[[[[],[[[[]]]],[]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => 0000000

[[[[],[[],[[[]]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => 0000000

[[[[],[[[],[]],[]]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => 0000000

[[[[],[[[[]]],[]]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => 0000000

[[[[],[[[],[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => 0000000

[[[[],[[[],[[]]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => 0000000

[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => 0000000

[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => 0000000

[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => 0000000

[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => 0000000

[[[[[]],[],[[],[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => 0000000

[[[[[]],[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => 0000000

[[[[[]],[[],[]],[]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => 0000000

[[[[[]],[[[]],[]]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => 0000000

[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => 0000000

[[[[[]],[[[[]]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => 0000000

[[[[[],[]],[],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => 0000000

[[[[[[]]],[],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => 0000000

[[[[[],[]],[[]],[]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => 0000000

[[[[[[],[]]],[],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => 0000000

[[[[[[[]]]],[],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => 0000000

[[[[[[],[]]],[[]]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => 0000000

[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => 0000000

[[[[[],[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => 0000000

[[[[[],[[[]]]],[]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => 0000000

[[[[[[[]]],[]],[]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => 0000000

[[[[[[],[],[]]],[]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => 0000000

[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => 0000000

[[[[[[[],[]]]],[]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => 0000000

[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => 0000000

[[[[[],[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => 0000000

[[[[[],[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => 0000000

[[[[[],[[]],[],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => 0000000

[[[[[],[[]],[[]]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => 0000000

[[[[[],[[[]]],[]]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => 0000000

[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => 0000000

[[[[[],[[[]],[]]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => 0000000

[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => 0000000

[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => 0000000

[[[[[[]],[[],[]]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => 0000000

[[[[[[],[]],[],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => 0000000

[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => 0000000

[[[[[[],[]],[[]]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => 0000000

[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => 0000000

[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => 0000000

[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => 0000000

[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => 0000000

[[[[[[],[[]],[]]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => 0000000

[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => 0000000

[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => 0000000

[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => 0000000

[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => 0000000

[[[[[[[],[]],[]]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => 0000000

[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => 0000000

[[[[[[[],[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => 0000000

[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => 0000000

[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => 0000000

[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => 0000000

[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => 0000000

Map

to Dyck path

Description

Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path to the depth of the tree.

Map

to non-crossing permutation

Description

Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..

Map

connectivity set

Description

The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.