Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001371: Binary words ⟶ ℤ
Values
[1,1,1] => [1,1] => [1] => 10 => 0
[2,1,1] => [1,1] => [1] => 10 => 0
[1,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[3,1,1] => [1,1] => [1] => 10 => 0
[2,2,1] => [2,1] => [1] => 10 => 0
[2,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[4,1,1] => [1,1] => [1] => 10 => 0
[3,2,1] => [2,1] => [1] => 10 => 0
[3,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[2,2,2] => [2,2] => [2] => 100 => 0
[2,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[5,1,1] => [1,1] => [1] => 10 => 0
[4,2,1] => [2,1] => [1] => 10 => 0
[4,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[3,3,1] => [3,1] => [1] => 10 => 0
[3,2,2] => [2,2] => [2] => 100 => 0
[3,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[2,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[6,1,1] => [1,1] => [1] => 10 => 0
[5,2,1] => [2,1] => [1] => 10 => 0
[5,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[4,3,1] => [3,1] => [1] => 10 => 0
[4,2,2] => [2,2] => [2] => 100 => 0
[4,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[3,3,2] => [3,2] => [2] => 100 => 0
[3,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[3,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[2,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[7,1,1] => [1,1] => [1] => 10 => 0
[6,2,1] => [2,1] => [1] => 10 => 0
[6,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[5,3,1] => [3,1] => [1] => 10 => 0
[5,2,2] => [2,2] => [2] => 100 => 0
[5,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[4,4,1] => [4,1] => [1] => 10 => 0
[4,3,2] => [3,2] => [2] => 100 => 0
[4,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[4,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[3,3,3] => [3,3] => [3] => 1000 => 0
[3,3,2,1] => [3,2,1] => [2,1] => 1010 => 0
[3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1110 => 0
[3,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 11010 => 0
[2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 101110 => 0
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[8,1,1] => [1,1] => [1] => 10 => 0
[7,2,1] => [2,1] => [1] => 10 => 0
[7,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[6,3,1] => [3,1] => [1] => 10 => 0
[6,2,2] => [2,2] => [2] => 100 => 0
[6,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[5,4,1] => [4,1] => [1] => 10 => 0
[5,3,2] => [3,2] => [2] => 100 => 0
[5,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[5,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[4,4,2] => [4,2] => [2] => 100 => 0
[4,4,1,1] => [4,1,1] => [1,1] => 110 => 0
[4,3,3] => [3,3] => [3] => 1000 => 0
[4,3,2,1] => [3,2,1] => [2,1] => 1010 => 0
[4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1110 => 0
[4,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[3,3,3,1] => [3,3,1] => [3,1] => 10010 => 0
[3,3,2,2] => [3,2,2] => [2,2] => 1100 => 0
[3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 10110 => 0
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 11110 => 0
[3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 11010 => 0
[3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 101110 => 0
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 11100 => 0
[2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 110110 => 0
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
>>> Load all 1237 entries. <<<[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[9,1,1] => [1,1] => [1] => 10 => 0
[8,2,1] => [2,1] => [1] => 10 => 0
[8,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[7,3,1] => [3,1] => [1] => 10 => 0
[7,2,2] => [2,2] => [2] => 100 => 0
[7,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[6,4,1] => [4,1] => [1] => 10 => 0
[6,3,2] => [3,2] => [2] => 100 => 0
[6,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[6,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[5,5,1] => [5,1] => [1] => 10 => 0
[5,4,2] => [4,2] => [2] => 100 => 0
[5,4,1,1] => [4,1,1] => [1,1] => 110 => 0
[5,3,3] => [3,3] => [3] => 1000 => 0
[5,3,2,1] => [3,2,1] => [2,1] => 1010 => 0
[5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1110 => 0
[5,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[4,4,3] => [4,3] => [3] => 1000 => 0
[4,4,2,1] => [4,2,1] => [2,1] => 1010 => 0
[4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1110 => 0
[4,3,3,1] => [3,3,1] => [3,1] => 10010 => 0
[4,3,2,2] => [3,2,2] => [2,2] => 1100 => 0
[4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 10110 => 0
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 11110 => 0
[4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 11010 => 0
[4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 101110 => 0
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[3,3,3,2] => [3,3,2] => [3,2] => 10100 => 0
[3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 100110 => 0
[3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 11010 => 0
[3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 101110 => 0
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 11100 => 0
[3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 110110 => 0
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 111010 => 0
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[10,1,1] => [1,1] => [1] => 10 => 0
[9,2,1] => [2,1] => [1] => 10 => 0
[9,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[8,3,1] => [3,1] => [1] => 10 => 0
[8,2,2] => [2,2] => [2] => 100 => 0
[8,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[8,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[7,4,1] => [4,1] => [1] => 10 => 0
[7,3,2] => [3,2] => [2] => 100 => 0
[7,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[7,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[6,5,1] => [5,1] => [1] => 10 => 0
[6,4,2] => [4,2] => [2] => 100 => 0
[6,4,1,1] => [4,1,1] => [1,1] => 110 => 0
[6,3,3] => [3,3] => [3] => 1000 => 0
[6,3,2,1] => [3,2,1] => [2,1] => 1010 => 0
[6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1110 => 0
[6,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[5,5,2] => [5,2] => [2] => 100 => 0
[5,5,1,1] => [5,1,1] => [1,1] => 110 => 0
[5,4,3] => [4,3] => [3] => 1000 => 0
[5,4,2,1] => [4,2,1] => [2,1] => 1010 => 0
[5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1110 => 0
[5,3,3,1] => [3,3,1] => [3,1] => 10010 => 0
[5,3,2,2] => [3,2,2] => [2,2] => 1100 => 0
[5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 10110 => 0
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 11110 => 0
[5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 11010 => 0
[5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 101110 => 0
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[4,4,4] => [4,4] => [4] => 10000 => 0
[4,4,3,1] => [4,3,1] => [3,1] => 10010 => 0
[4,4,2,2] => [4,2,2] => [2,2] => 1100 => 0
[4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 10110 => 0
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 11110 => 0
[4,3,3,2] => [3,3,2] => [3,2] => 10100 => 0
[4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 100110 => 0
[4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 11010 => 0
[4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 101110 => 0
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 11100 => 0
[4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 110110 => 0
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[3,3,3,3] => [3,3,3] => [3,3] => 11000 => 0
[3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 101010 => 0
[3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 11100 => 0
[3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 110110 => 0
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 111010 => 0
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 111100 => 0
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[11,1,1] => [1,1] => [1] => 10 => 0
[10,2,1] => [2,1] => [1] => 10 => 0
[10,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[9,3,1] => [3,1] => [1] => 10 => 0
[9,2,2] => [2,2] => [2] => 100 => 0
[9,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[9,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[8,4,1] => [4,1] => [1] => 10 => 0
[8,3,2] => [3,2] => [2] => 100 => 0
[8,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[8,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[8,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[7,5,1] => [5,1] => [1] => 10 => 0
[7,4,2] => [4,2] => [2] => 100 => 0
[7,4,1,1] => [4,1,1] => [1,1] => 110 => 0
[7,3,3] => [3,3] => [3] => 1000 => 0
[7,3,2,1] => [3,2,1] => [2,1] => 1010 => 0
[7,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1110 => 0
[7,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[7,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[6,6,1] => [6,1] => [1] => 10 => 0
[6,5,2] => [5,2] => [2] => 100 => 0
[6,5,1,1] => [5,1,1] => [1,1] => 110 => 0
[6,4,3] => [4,3] => [3] => 1000 => 0
[6,4,2,1] => [4,2,1] => [2,1] => 1010 => 0
[6,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1110 => 0
[6,3,3,1] => [3,3,1] => [3,1] => 10010 => 0
[6,3,2,2] => [3,2,2] => [2,2] => 1100 => 0
[6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 10110 => 0
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 11110 => 0
[6,2,2,2,1] => [2,2,2,1] => [2,2,1] => 11010 => 0
[6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 101110 => 0
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[5,5,3] => [5,3] => [3] => 1000 => 0
[5,5,2,1] => [5,2,1] => [2,1] => 1010 => 0
[5,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1110 => 0
[5,4,4] => [4,4] => [4] => 10000 => 0
[5,4,3,1] => [4,3,1] => [3,1] => 10010 => 0
[5,4,2,2] => [4,2,2] => [2,2] => 1100 => 0
[5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 10110 => 0
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 11110 => 0
[5,3,3,2] => [3,3,2] => [3,2] => 10100 => 0
[5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 100110 => 0
[5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 11010 => 0
[5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 101110 => 0
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[5,2,2,2,2] => [2,2,2,2] => [2,2,2] => 11100 => 0
[5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 110110 => 0
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[4,4,4,1] => [4,4,1] => [4,1] => 100010 => 0
[4,4,3,2] => [4,3,2] => [3,2] => 10100 => 0
[4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 100110 => 0
[4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 11010 => 0
[4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 101110 => 0
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[4,3,3,3] => [3,3,3] => [3,3] => 11000 => 0
[4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 101010 => 0
[4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 11100 => 0
[4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 110110 => 0
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 111010 => 0
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 110010 => 0
[3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 101100 => 0
[3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 0
[3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 111010 => 0
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 111100 => 0
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 0
[2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 0
[12,1,1] => [1,1] => [1] => 10 => 0
[11,2,1] => [2,1] => [1] => 10 => 0
[11,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[10,3,1] => [3,1] => [1] => 10 => 0
[10,2,2] => [2,2] => [2] => 100 => 0
[10,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[10,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[9,4,1] => [4,1] => [1] => 10 => 0
[9,3,2] => [3,2] => [2] => 100 => 0
[9,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[9,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[9,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[8,5,1] => [5,1] => [1] => 10 => 0
[8,4,2] => [4,2] => [2] => 100 => 0
[8,4,1,1] => [4,1,1] => [1,1] => 110 => 0
[8,3,3] => [3,3] => [3] => 1000 => 0
[8,3,2,1] => [3,2,1] => [2,1] => 1010 => 0
[8,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1110 => 0
[8,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[8,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[7,6,1] => [6,1] => [1] => 10 => 0
[7,5,2] => [5,2] => [2] => 100 => 0
[7,5,1,1] => [5,1,1] => [1,1] => 110 => 0
[7,4,3] => [4,3] => [3] => 1000 => 0
[7,4,2,1] => [4,2,1] => [2,1] => 1010 => 0
[7,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1110 => 0
[7,3,3,1] => [3,3,1] => [3,1] => 10010 => 0
[7,3,2,2] => [3,2,2] => [2,2] => 1100 => 0
[7,3,2,1,1] => [3,2,1,1] => [2,1,1] => 10110 => 0
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 11110 => 0
[7,2,2,2,1] => [2,2,2,1] => [2,2,1] => 11010 => 0
[7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 101110 => 0
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[6,6,2] => [6,2] => [2] => 100 => 0
[6,6,1,1] => [6,1,1] => [1,1] => 110 => 0
[6,5,3] => [5,3] => [3] => 1000 => 0
[6,5,2,1] => [5,2,1] => [2,1] => 1010 => 0
[6,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1110 => 0
[6,4,4] => [4,4] => [4] => 10000 => 0
[6,4,3,1] => [4,3,1] => [3,1] => 10010 => 0
[6,4,2,2] => [4,2,2] => [2,2] => 1100 => 0
[6,4,2,1,1] => [4,2,1,1] => [2,1,1] => 10110 => 0
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 11110 => 0
[6,3,3,2] => [3,3,2] => [3,2] => 10100 => 0
[6,3,3,1,1] => [3,3,1,1] => [3,1,1] => 100110 => 0
[6,3,2,2,1] => [3,2,2,1] => [2,2,1] => 11010 => 0
[6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 101110 => 0
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 11100 => 0
[6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 110110 => 0
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[5,5,4] => [5,4] => [4] => 10000 => 0
[5,5,3,1] => [5,3,1] => [3,1] => 10010 => 0
[5,5,2,2] => [5,2,2] => [2,2] => 1100 => 0
[5,5,2,1,1] => [5,2,1,1] => [2,1,1] => 10110 => 0
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 11110 => 0
[5,4,4,1] => [4,4,1] => [4,1] => 100010 => 0
[5,4,3,2] => [4,3,2] => [3,2] => 10100 => 0
[5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 100110 => 0
[5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 11010 => 0
[5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 101110 => 0
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[5,3,3,3] => [3,3,3] => [3,3] => 11000 => 0
[5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 101010 => 0
[5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[5,3,2,2,2] => [3,2,2,2] => [2,2,2] => 11100 => 0
[5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 110110 => 0
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 111010 => 0
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[4,4,4,2] => [4,4,2] => [4,2] => 100100 => 0
[4,4,4,1,1] => [4,4,1,1] => [4,1,1] => 1000110 => 0
[4,4,3,3] => [4,3,3] => [3,3] => 11000 => 0
[4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 101010 => 0
[4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[4,4,2,2,2] => [4,2,2,2] => [2,2,2] => 11100 => 0
[4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 110110 => 0
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[4,3,3,3,1] => [3,3,3,1] => [3,3,1] => 110010 => 0
[4,3,3,2,2] => [3,3,2,2] => [3,2,2] => 101100 => 0
[4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 0
[4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 111010 => 0
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 111100 => 0
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 110100 => 0
[3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 1100110 => 0
[3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 0
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 0
[3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 111100 => 0
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 0
[3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 0
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0
[2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 0
[2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 0
[13,1,1] => [1,1] => [1] => 10 => 0
[12,2,1] => [2,1] => [1] => 10 => 0
[12,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[11,3,1] => [3,1] => [1] => 10 => 0
[11,2,2] => [2,2] => [2] => 100 => 0
[11,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[11,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[10,4,1] => [4,1] => [1] => 10 => 0
[10,3,2] => [3,2] => [2] => 100 => 0
[10,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[10,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[10,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[9,5,1] => [5,1] => [1] => 10 => 0
[9,4,2] => [4,2] => [2] => 100 => 0
[9,4,1,1] => [4,1,1] => [1,1] => 110 => 0
[9,3,3] => [3,3] => [3] => 1000 => 0
[9,3,2,1] => [3,2,1] => [2,1] => 1010 => 0
[9,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1110 => 0
[9,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[9,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[8,6,1] => [6,1] => [1] => 10 => 0
[8,5,2] => [5,2] => [2] => 100 => 0
[8,5,1,1] => [5,1,1] => [1,1] => 110 => 0
[8,4,3] => [4,3] => [3] => 1000 => 0
[8,4,2,1] => [4,2,1] => [2,1] => 1010 => 0
[8,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1110 => 0
[8,3,3,1] => [3,3,1] => [3,1] => 10010 => 0
[8,3,2,2] => [3,2,2] => [2,2] => 1100 => 0
[8,3,2,1,1] => [3,2,1,1] => [2,1,1] => 10110 => 0
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 11110 => 0
[8,2,2,2,1] => [2,2,2,1] => [2,2,1] => 11010 => 0
[8,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 101110 => 0
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[7,7,1] => [7,1] => [1] => 10 => 0
[7,6,2] => [6,2] => [2] => 100 => 0
[7,6,1,1] => [6,1,1] => [1,1] => 110 => 0
[7,5,3] => [5,3] => [3] => 1000 => 0
[7,5,2,1] => [5,2,1] => [2,1] => 1010 => 0
[7,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1110 => 0
[7,4,4] => [4,4] => [4] => 10000 => 0
[7,4,3,1] => [4,3,1] => [3,1] => 10010 => 0
[7,4,2,2] => [4,2,2] => [2,2] => 1100 => 0
[7,4,2,1,1] => [4,2,1,1] => [2,1,1] => 10110 => 0
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 11110 => 0
[7,3,3,2] => [3,3,2] => [3,2] => 10100 => 0
[7,3,3,1,1] => [3,3,1,1] => [3,1,1] => 100110 => 0
[7,3,2,2,1] => [3,2,2,1] => [2,2,1] => 11010 => 0
[7,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 101110 => 0
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[7,2,2,2,2] => [2,2,2,2] => [2,2,2] => 11100 => 0
[7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 110110 => 0
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[6,6,3] => [6,3] => [3] => 1000 => 0
[6,6,2,1] => [6,2,1] => [2,1] => 1010 => 0
[6,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1110 => 0
[6,5,4] => [5,4] => [4] => 10000 => 0
[6,5,3,1] => [5,3,1] => [3,1] => 10010 => 0
[6,5,2,2] => [5,2,2] => [2,2] => 1100 => 0
[6,5,2,1,1] => [5,2,1,1] => [2,1,1] => 10110 => 0
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 11110 => 0
[6,4,4,1] => [4,4,1] => [4,1] => 100010 => 0
[6,4,3,2] => [4,3,2] => [3,2] => 10100 => 0
[6,4,3,1,1] => [4,3,1,1] => [3,1,1] => 100110 => 0
[6,4,2,2,1] => [4,2,2,1] => [2,2,1] => 11010 => 0
[6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 101110 => 0
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[6,3,3,3] => [3,3,3] => [3,3] => 11000 => 0
[6,3,3,2,1] => [3,3,2,1] => [3,2,1] => 101010 => 0
[6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[6,3,2,2,2] => [3,2,2,2] => [2,2,2] => 11100 => 0
[6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 110110 => 0
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 111010 => 0
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[5,5,5] => [5,5] => [5] => 100000 => 0
[5,5,4,1] => [5,4,1] => [4,1] => 100010 => 0
[5,5,3,2] => [5,3,2] => [3,2] => 10100 => 0
[5,5,3,1,1] => [5,3,1,1] => [3,1,1] => 100110 => 0
[5,5,2,2,1] => [5,2,2,1] => [2,2,1] => 11010 => 0
[5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 101110 => 0
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[5,4,4,2] => [4,4,2] => [4,2] => 100100 => 0
[5,4,4,1,1] => [4,4,1,1] => [4,1,1] => 1000110 => 0
[5,4,3,3] => [4,3,3] => [3,3] => 11000 => 0
[5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 101010 => 0
[5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[5,4,2,2,2] => [4,2,2,2] => [2,2,2] => 11100 => 0
[5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 110110 => 0
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[5,3,3,3,1] => [3,3,3,1] => [3,3,1] => 110010 => 0
[5,3,3,2,2] => [3,3,2,2] => [3,2,2] => 101100 => 0
[5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 0
[5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 111010 => 0
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 111100 => 0
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[4,4,4,3] => [4,4,3] => [4,3] => 101000 => 0
[4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 1001010 => 0
[4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 10001110 => 0
[4,4,3,3,1] => [4,3,3,1] => [3,3,1] => 110010 => 0
[4,4,3,2,2] => [4,3,2,2] => [3,2,2] => 101100 => 0
[4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 0
[4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 111010 => 0
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[4,3,3,3,2] => [3,3,3,2] => [3,3,2] => 110100 => 0
[4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 1100110 => 0
[4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 0
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 0
[4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 111100 => 0
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[4,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 0
[4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 0
[3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 111000 => 0
[3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 0
[3,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 1011100 => 0
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 0
[3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 0
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 0
[3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 0
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0
[3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 0
[3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 0
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 0
[2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 111101110 => 0
[14,1,1] => [1,1] => [1] => 10 => 0
[13,2,1] => [2,1] => [1] => 10 => 0
[13,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[12,3,1] => [3,1] => [1] => 10 => 0
[12,2,2] => [2,2] => [2] => 100 => 0
[12,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[12,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[11,4,1] => [4,1] => [1] => 10 => 0
[11,3,2] => [3,2] => [2] => 100 => 0
[11,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[11,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[11,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[10,5,1] => [5,1] => [1] => 10 => 0
[10,4,2] => [4,2] => [2] => 100 => 0
[10,4,1,1] => [4,1,1] => [1,1] => 110 => 0
[10,3,3] => [3,3] => [3] => 1000 => 0
[10,3,2,1] => [3,2,1] => [2,1] => 1010 => 0
[10,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1110 => 0
[10,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[10,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[9,6,1] => [6,1] => [1] => 10 => 0
[9,5,2] => [5,2] => [2] => 100 => 0
[9,5,1,1] => [5,1,1] => [1,1] => 110 => 0
[9,4,3] => [4,3] => [3] => 1000 => 0
[9,4,2,1] => [4,2,1] => [2,1] => 1010 => 0
[9,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1110 => 0
[9,3,3,1] => [3,3,1] => [3,1] => 10010 => 0
[9,3,2,2] => [3,2,2] => [2,2] => 1100 => 0
[9,3,2,1,1] => [3,2,1,1] => [2,1,1] => 10110 => 0
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 11110 => 0
[9,2,2,2,1] => [2,2,2,1] => [2,2,1] => 11010 => 0
[9,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 101110 => 0
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[8,7,1] => [7,1] => [1] => 10 => 0
[8,6,2] => [6,2] => [2] => 100 => 0
[8,6,1,1] => [6,1,1] => [1,1] => 110 => 0
[8,5,3] => [5,3] => [3] => 1000 => 0
[8,5,2,1] => [5,2,1] => [2,1] => 1010 => 0
[8,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1110 => 0
[8,4,4] => [4,4] => [4] => 10000 => 0
[8,4,3,1] => [4,3,1] => [3,1] => 10010 => 0
[8,4,2,2] => [4,2,2] => [2,2] => 1100 => 0
[8,4,2,1,1] => [4,2,1,1] => [2,1,1] => 10110 => 0
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 11110 => 0
[8,3,3,2] => [3,3,2] => [3,2] => 10100 => 0
[8,3,3,1,1] => [3,3,1,1] => [3,1,1] => 100110 => 0
[8,3,2,2,1] => [3,2,2,1] => [2,2,1] => 11010 => 0
[8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 101110 => 0
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[8,2,2,2,2] => [2,2,2,2] => [2,2,2] => 11100 => 0
[8,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 110110 => 0
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[7,7,2] => [7,2] => [2] => 100 => 0
[7,7,1,1] => [7,1,1] => [1,1] => 110 => 0
[7,6,3] => [6,3] => [3] => 1000 => 0
[7,6,2,1] => [6,2,1] => [2,1] => 1010 => 0
[7,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1110 => 0
[7,5,4] => [5,4] => [4] => 10000 => 0
[7,5,3,1] => [5,3,1] => [3,1] => 10010 => 0
[7,5,2,2] => [5,2,2] => [2,2] => 1100 => 0
[7,5,2,1,1] => [5,2,1,1] => [2,1,1] => 10110 => 0
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 11110 => 0
[7,4,4,1] => [4,4,1] => [4,1] => 100010 => 0
[7,4,3,2] => [4,3,2] => [3,2] => 10100 => 0
[7,4,3,1,1] => [4,3,1,1] => [3,1,1] => 100110 => 0
[7,4,2,2,1] => [4,2,2,1] => [2,2,1] => 11010 => 0
[7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 101110 => 0
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[7,3,3,3] => [3,3,3] => [3,3] => 11000 => 0
[7,3,3,2,1] => [3,3,2,1] => [3,2,1] => 101010 => 0
[7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[7,3,2,2,2] => [3,2,2,2] => [2,2,2] => 11100 => 0
[7,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 110110 => 0
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 111010 => 0
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[6,6,4] => [6,4] => [4] => 10000 => 0
[6,6,3,1] => [6,3,1] => [3,1] => 10010 => 0
[6,6,2,2] => [6,2,2] => [2,2] => 1100 => 0
[6,6,2,1,1] => [6,2,1,1] => [2,1,1] => 10110 => 0
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 11110 => 0
[6,5,5] => [5,5] => [5] => 100000 => 0
[6,5,4,1] => [5,4,1] => [4,1] => 100010 => 0
[6,5,3,2] => [5,3,2] => [3,2] => 10100 => 0
[6,5,3,1,1] => [5,3,1,1] => [3,1,1] => 100110 => 0
[6,5,2,2,1] => [5,2,2,1] => [2,2,1] => 11010 => 0
[6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 101110 => 0
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[6,4,4,2] => [4,4,2] => [4,2] => 100100 => 0
[6,4,4,1,1] => [4,4,1,1] => [4,1,1] => 1000110 => 0
[6,4,3,3] => [4,3,3] => [3,3] => 11000 => 0
[6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 101010 => 0
[6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[6,4,2,2,2] => [4,2,2,2] => [2,2,2] => 11100 => 0
[6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 110110 => 0
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[6,3,3,3,1] => [3,3,3,1] => [3,3,1] => 110010 => 0
[6,3,3,2,2] => [3,3,2,2] => [3,2,2] => 101100 => 0
[6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 0
[6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 111010 => 0
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 111100 => 0
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[5,5,5,1] => [5,5,1] => [5,1] => 1000010 => 0
[5,5,4,2] => [5,4,2] => [4,2] => 100100 => 0
[5,5,4,1,1] => [5,4,1,1] => [4,1,1] => 1000110 => 0
[5,5,3,3] => [5,3,3] => [3,3] => 11000 => 0
[5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 101010 => 0
[5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[5,5,2,2,2] => [5,2,2,2] => [2,2,2] => 11100 => 0
[5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 110110 => 0
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[5,4,4,3] => [4,4,3] => [4,3] => 101000 => 0
[5,4,4,2,1] => [4,4,2,1] => [4,2,1] => 1001010 => 0
[5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 10001110 => 0
[5,4,3,3,1] => [4,3,3,1] => [3,3,1] => 110010 => 0
[5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 101100 => 0
[5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 0
[5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 111010 => 0
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[5,3,3,3,2] => [3,3,3,2] => [3,3,2] => 110100 => 0
[5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 1100110 => 0
[5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 0
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 0
[5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 111100 => 0
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[5,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 0
[5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 0
[4,4,4,4] => [4,4,4] => [4,4] => 110000 => 0
[4,4,4,3,1] => [4,4,3,1] => [4,3,1] => 1010010 => 0
[4,4,4,2,2] => [4,4,2,2] => [4,2,2] => 1001100 => 0
[4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 10010110 => 0
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 100011110 => 0
[4,4,3,3,2] => [4,3,3,2] => [3,3,2] => 110100 => 0
[4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 1100110 => 0
[4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 0
[4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 0
[4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 111100 => 0
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[4,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[4,3,3,3,3] => [3,3,3,3] => [3,3,3] => 111000 => 0
[4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 0
[4,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 1011100 => 0
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 0
[4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 0
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 0
[4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 0
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0
[4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 0
[4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 0
[3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 1110010 => 0
[3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 1101100 => 0
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 0
[3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 0
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 0
[3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 101101110 => 0
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0
[3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 0
[3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 0
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 0
[3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 111101110 => 0
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 0
[2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 111110110 => 0
[15,1,1] => [1,1] => [1] => 10 => 0
[14,2,1] => [2,1] => [1] => 10 => 0
[14,1,1,1] => [1,1,1] => [1,1] => 110 => 0
[13,3,1] => [3,1] => [1] => 10 => 0
[13,2,2] => [2,2] => [2] => 100 => 0
[13,2,1,1] => [2,1,1] => [1,1] => 110 => 0
[13,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1110 => 0
[12,4,1] => [4,1] => [1] => 10 => 0
[12,3,2] => [3,2] => [2] => 100 => 0
[12,3,1,1] => [3,1,1] => [1,1] => 110 => 0
[12,2,2,1] => [2,2,1] => [2,1] => 1010 => 0
[12,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1110 => 0
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 11110 => 0
[11,5,1] => [5,1] => [1] => 10 => 0
[11,4,2] => [4,2] => [2] => 100 => 0
[11,4,1,1] => [4,1,1] => [1,1] => 110 => 0
[11,3,3] => [3,3] => [3] => 1000 => 0
[11,3,2,1] => [3,2,1] => [2,1] => 1010 => 0
[11,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1110 => 0
[11,2,2,2] => [2,2,2] => [2,2] => 1100 => 0
[11,2,2,1,1] => [2,2,1,1] => [2,1,1] => 10110 => 0
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 11110 => 0
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[10,6,1] => [6,1] => [1] => 10 => 0
[10,5,2] => [5,2] => [2] => 100 => 0
[10,5,1,1] => [5,1,1] => [1,1] => 110 => 0
[10,4,3] => [4,3] => [3] => 1000 => 0
[10,4,2,1] => [4,2,1] => [2,1] => 1010 => 0
[10,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1110 => 0
[10,3,3,1] => [3,3,1] => [3,1] => 10010 => 0
[10,3,2,2] => [3,2,2] => [2,2] => 1100 => 0
[10,3,2,1,1] => [3,2,1,1] => [2,1,1] => 10110 => 0
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 11110 => 0
[10,2,2,2,1] => [2,2,2,1] => [2,2,1] => 11010 => 0
[10,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 101110 => 0
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[9,7,1] => [7,1] => [1] => 10 => 0
[9,6,2] => [6,2] => [2] => 100 => 0
[9,6,1,1] => [6,1,1] => [1,1] => 110 => 0
[9,5,3] => [5,3] => [3] => 1000 => 0
[9,5,2,1] => [5,2,1] => [2,1] => 1010 => 0
[9,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1110 => 0
[9,4,4] => [4,4] => [4] => 10000 => 0
[9,4,3,1] => [4,3,1] => [3,1] => 10010 => 0
[9,4,2,2] => [4,2,2] => [2,2] => 1100 => 0
[9,4,2,1,1] => [4,2,1,1] => [2,1,1] => 10110 => 0
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 11110 => 0
[9,3,3,2] => [3,3,2] => [3,2] => 10100 => 0
[9,3,3,1,1] => [3,3,1,1] => [3,1,1] => 100110 => 0
[9,3,2,2,1] => [3,2,2,1] => [2,2,1] => 11010 => 0
[9,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 101110 => 0
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[9,2,2,2,2] => [2,2,2,2] => [2,2,2] => 11100 => 0
[9,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 110110 => 0
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[8,8,1] => [8,1] => [1] => 10 => 0
[8,7,2] => [7,2] => [2] => 100 => 0
[8,7,1,1] => [7,1,1] => [1,1] => 110 => 0
[8,6,3] => [6,3] => [3] => 1000 => 0
[8,6,2,1] => [6,2,1] => [2,1] => 1010 => 0
[8,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1110 => 0
[8,5,4] => [5,4] => [4] => 10000 => 0
[8,5,3,1] => [5,3,1] => [3,1] => 10010 => 0
[8,5,2,2] => [5,2,2] => [2,2] => 1100 => 0
[8,5,2,1,1] => [5,2,1,1] => [2,1,1] => 10110 => 0
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 11110 => 0
[8,4,4,1] => [4,4,1] => [4,1] => 100010 => 0
[8,4,3,2] => [4,3,2] => [3,2] => 10100 => 0
[8,4,3,1,1] => [4,3,1,1] => [3,1,1] => 100110 => 0
[8,4,2,2,1] => [4,2,2,1] => [2,2,1] => 11010 => 0
[8,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 101110 => 0
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[8,3,3,3] => [3,3,3] => [3,3] => 11000 => 0
[8,3,3,2,1] => [3,3,2,1] => [3,2,1] => 101010 => 0
[8,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[8,3,2,2,2] => [3,2,2,2] => [2,2,2] => 11100 => 0
[8,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 110110 => 0
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[8,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 111010 => 0
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[7,7,3] => [7,3] => [3] => 1000 => 0
[7,7,2,1] => [7,2,1] => [2,1] => 1010 => 0
[7,7,1,1,1] => [7,1,1,1] => [1,1,1] => 1110 => 0
[7,6,4] => [6,4] => [4] => 10000 => 0
[7,6,3,1] => [6,3,1] => [3,1] => 10010 => 0
[7,6,2,2] => [6,2,2] => [2,2] => 1100 => 0
[7,6,2,1,1] => [6,2,1,1] => [2,1,1] => 10110 => 0
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 11110 => 0
[7,5,5] => [5,5] => [5] => 100000 => 0
[7,5,4,1] => [5,4,1] => [4,1] => 100010 => 0
[7,5,3,2] => [5,3,2] => [3,2] => 10100 => 0
[7,5,3,1,1] => [5,3,1,1] => [3,1,1] => 100110 => 0
[7,5,2,2,1] => [5,2,2,1] => [2,2,1] => 11010 => 0
[7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 101110 => 0
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[7,4,4,2] => [4,4,2] => [4,2] => 100100 => 0
[7,4,4,1,1] => [4,4,1,1] => [4,1,1] => 1000110 => 0
[7,4,3,3] => [4,3,3] => [3,3] => 11000 => 0
[7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 101010 => 0
[7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[7,4,2,2,2] => [4,2,2,2] => [2,2,2] => 11100 => 0
[7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 110110 => 0
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[7,3,3,3,1] => [3,3,3,1] => [3,3,1] => 110010 => 0
[7,3,3,2,2] => [3,3,2,2] => [3,2,2] => 101100 => 0
[7,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 0
[7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 111010 => 0
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 111100 => 0
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[6,6,5] => [6,5] => [5] => 100000 => 0
[6,6,4,1] => [6,4,1] => [4,1] => 100010 => 0
[6,6,3,2] => [6,3,2] => [3,2] => 10100 => 0
[6,6,3,1,1] => [6,3,1,1] => [3,1,1] => 100110 => 0
[6,6,2,2,1] => [6,2,2,1] => [2,2,1] => 11010 => 0
[6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 101110 => 0
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[6,5,5,1] => [5,5,1] => [5,1] => 1000010 => 0
[6,5,4,2] => [5,4,2] => [4,2] => 100100 => 0
[6,5,4,1,1] => [5,4,1,1] => [4,1,1] => 1000110 => 0
[6,5,3,3] => [5,3,3] => [3,3] => 11000 => 0
[6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 101010 => 0
[6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 1001110 => 0
[6,5,2,2,2] => [5,2,2,2] => [2,2,2] => 11100 => 0
[6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 110110 => 0
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[6,4,4,3] => [4,4,3] => [4,3] => 101000 => 0
[6,4,4,2,1] => [4,4,2,1] => [4,2,1] => 1001010 => 0
[6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 10001110 => 0
[6,4,3,3,1] => [4,3,3,1] => [3,3,1] => 110010 => 0
[6,4,3,2,2] => [4,3,2,2] => [3,2,2] => 101100 => 0
[6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 0
[6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 111010 => 0
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[6,3,3,3,2] => [3,3,3,2] => [3,3,2] => 110100 => 0
[6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 1100110 => 0
[6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 0
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 0
[6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 111100 => 0
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[6,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 0
[6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 0
[5,5,5,2] => [5,5,2] => [5,2] => 1000100 => 0
[5,5,5,1,1] => [5,5,1,1] => [5,1,1] => 10000110 => 0
[5,5,4,3] => [5,4,3] => [4,3] => 101000 => 0
[5,5,4,2,1] => [5,4,2,1] => [4,2,1] => 1001010 => 0
[5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 10001110 => 0
[5,5,3,3,1] => [5,3,3,1] => [3,3,1] => 110010 => 0
[5,5,3,2,2] => [5,3,2,2] => [3,2,2] => 101100 => 0
[5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 0
[5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 111010 => 0
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0
[5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 0
[5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 0
[5,4,4,4] => [4,4,4] => [4,4] => 110000 => 0
[5,4,4,3,1] => [4,4,3,1] => [4,3,1] => 1010010 => 0
[5,4,4,2,2] => [4,4,2,2] => [4,2,2] => 1001100 => 0
[5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 10010110 => 0
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 100011110 => 0
[5,4,3,3,2] => [4,3,3,2] => [3,3,2] => 110100 => 0
[5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 1100110 => 0
[5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 0
[5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 0
[5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 111100 => 0
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0
[5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 0
[5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 0
[5,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 0
[5,3,3,3,3] => [3,3,3,3] => [3,3,3] => 111000 => 0
[5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 0
[5,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 1011100 => 0
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 0
[5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 0
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 0
[5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 0
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0
[5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 0
[5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 0
[4,4,4,4,1] => [4,4,4,1] => [4,4,1] => 1100010 => 0
[4,4,4,3,2] => [4,4,3,2] => [4,3,2] => 1010100 => 0
[4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10100110 => 0
[4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 10011010 => 0
[4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => 100101110 => 0
[4,4,3,3,3] => [4,3,3,3] => [3,3,3] => 111000 => 0
[4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 0
[4,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 1011100 => 0
[4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 0
[4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 0
[4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 0
[4,4,2,2,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 0
[4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 1110010 => 0
[4,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 1101100 => 0
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 0
[4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 0
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 0
[4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 101101110 => 0
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0
[4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 0
[4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 0
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 0
[4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 111101110 => 0
[3,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 1110100 => 0
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => 11100110 => 0
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [3,3,2,2,1] => 11011010 => 0
[3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => 110101110 => 0
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 0
[3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => 101110110 => 0
[3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 0
[3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 111101110 => 0
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 0
[3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 111110110 => 0
[2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 111111010 => 0
[6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[6,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[5,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[6,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[6,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[6,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 10011010 => 0
[5,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 10011010 => 0
[6,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 10011010 => 0
[5,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 10011010 => 0
[6,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[5,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[6,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 111010 => 0
[6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 10100110 => 0
[5,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 10100110 => 0
[6,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10100110 => 0
[5,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10100110 => 0
[6,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 1100110 => 0
[5,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 1100110 => 0
[6,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 1100110 => 0
[6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 10010110 => 0
[5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 10010110 => 0
[6,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 10010110 => 0
[6,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 10001110 => 0
[6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 1010100 => 0
[5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 1010100 => 0
[6,4,4,3,2] => [4,4,3,2] => [4,3,2] => 1010100 => 0
[5,4,4,3,2] => [4,4,3,2] => [4,3,2] => 1010100 => 0
[6,5,3,3,2] => [5,3,3,2] => [3,3,2] => 110100 => 0
[5,5,3,3,2] => [5,3,3,2] => [3,3,2] => 110100 => 0
[6,4,3,3,2] => [4,3,3,2] => [3,3,2] => 110100 => 0
[6,5,4,2,2] => [5,4,2,2] => [4,2,2] => 1001100 => 0
[5,5,4,2,2] => [5,4,2,2] => [4,2,2] => 1001100 => 0
[6,4,4,2,2] => [4,4,2,2] => [4,2,2] => 1001100 => 0
[6,5,3,2,2] => [5,3,2,2] => [3,2,2] => 101100 => 0
[6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 1010010 => 0
[5,5,4,3,1] => [5,4,3,1] => [4,3,1] => 1010010 => 0
[6,4,4,3,1] => [4,4,3,1] => [4,3,1] => 1010010 => 0
[6,5,3,3,1] => [5,3,3,1] => [3,3,1] => 110010 => 0
[6,5,4,2,1] => [5,4,2,1] => [4,2,1] => 1001010 => 0
[6,5,4,3] => [5,4,3] => [4,3] => 101000 => 0
[7,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[6,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[7,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[6,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[5,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[7,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[6,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[5,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[4,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[6,5,4,3,3,2,1] => [5,4,3,3,2,1] => [4,3,3,2,1] => 101101010 => 0
[6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 0
[6,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 0
[5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 0
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 0
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 0
[6,5,4,4,2,2,1] => [5,4,4,2,2,1] => [4,4,2,2,1] => 110011010 => 0
[6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => 101011010 => 0
[5,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => 101011010 => 0
[6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => 100111010 => 0
[6,5,3,2,2,2,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 0
[6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 0
[5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 0
[6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0
[4,4,4,4,2,1,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => 110010110 => 0
[6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 101010110 => 0
[5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 101010110 => 0
[5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => 101010110 => 0
[6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => 101001110 => 0
[7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 100101110 => 0
[6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 100101110 => 0
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 0
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 0
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 0
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 100011110 => 0
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 0
[7,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 101010100 => 0
[6,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 101010100 => 0
[7,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => 101010100 => 0
[6,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => 101010100 => 0
[5,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => 101010100 => 0
[7,6,4,4,3,2] => [6,4,4,3,2] => [4,4,3,2] => 11010100 => 0
[6,5,4,4,3,2] => [5,4,4,3,2] => [4,4,3,2] => 11010100 => 0
[6,5,4,3,3,2] => [5,4,3,3,2] => [4,3,3,2] => 10110100 => 0
[5,4,3,3,3,2] => [4,3,3,3,2] => [3,3,3,2] => 1110100 => 0
[4,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 1110100 => 0
[6,5,4,3,2,2] => [5,4,3,2,2] => [4,3,2,2] => 10101100 => 0
[4,4,4,3,2,2] => [4,4,3,2,2] => [4,3,2,2] => 10101100 => 0
[7,6,5,2,2,2] => [6,5,2,2,2] => [5,2,2,2] => 100011100 => 0
[6,5,4,2,2,2] => [5,4,2,2,2] => [4,2,2,2] => 10011100 => 0
[5,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 1011100 => 0
[6,6,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => 111100 => 0
[7,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => 101010010 => 0
[6,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => 101010010 => 0
[6,5,5,4,3,1] => [5,5,4,3,1] => [5,4,3,1] => 101010010 => 0
[4,4,4,4,3,1] => [4,4,4,3,1] => [4,4,3,1] => 11010010 => 0
[7,6,5,4,2,1] => [6,5,4,2,1] => [5,4,2,1] => 101001010 => 0
[5,5,5,4,2,1] => [5,5,4,2,1] => [5,4,2,1] => 101001010 => 0
[4,4,4,4,2,1] => [4,4,4,2,1] => [4,4,2,1] => 11001010 => 0
[7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 100101010 => 0
[6,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 100101010 => 0
[5,5,5,3,2,1] => [5,5,3,2,1] => [5,3,2,1] => 100101010 => 0
[7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[6,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[7,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[7,6,3,3,2,1] => [6,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[7,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[7,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 1101010 => 0
[7,6,5,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => 100011010 => 0
[7,6,3,2,2,1] => [6,3,2,2,1] => [3,2,2,1] => 1011010 => 0
[7,6,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => 111010 => 0
[7,6,5,4,1,1] => [6,5,4,1,1] => [5,4,1,1] => 101000110 => 0
[7,6,5,2,1,1] => [6,5,2,1,1] => [5,2,1,1] => 100010110 => 0
[7,6,3,2,1,1] => [6,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[7,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 1010110 => 0
[7,6,5,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => 100001110 => 0
[7,6,5,4,3] => [6,5,4,3] => [5,4,3] => 10101000 => 0
[6,6,5,4,3] => [6,5,4,3] => [5,4,3] => 10101000 => 0
[6,5,5,4,3] => [5,5,4,3] => [5,4,3] => 10101000 => 0
[5,4,4,4,3] => [4,4,4,3] => [4,4,3] => 1101000 => 0
[5,4,3,3,3] => [4,3,3,3] => [3,3,3] => 111000 => 0
[7,3,3,3,3] => [3,3,3,3] => [3,3,3] => 111000 => 0
[7,6,5,4,2] => [6,5,4,2] => [5,4,2] => 10100100 => 0
[4,4,4,4,2] => [4,4,4,2] => [4,4,2] => 1100100 => 0
[7,6,5,3,2] => [6,5,3,2] => [5,3,2] => 10010100 => 0
[7,6,4,3,2] => [6,4,3,2] => [4,3,2] => 1010100 => 0
[7,5,4,3,2] => [5,4,3,2] => [4,3,2] => 1010100 => 0
[7,6,5,4,1] => [6,5,4,1] => [5,4,1] => 10100010 => 0
[7,5,4,3,1] => [5,4,3,1] => [4,3,1] => 1010010 => 0
[7,6,5,2,1] => [6,5,2,1] => [5,2,1] => 10001010 => 0
[6,6,5,2,1] => [6,5,2,1] => [5,2,1] => 10001010 => 0
[7,6,4,2,1] => [6,4,2,1] => [4,2,1] => 1001010 => 0
[6,6,4,2,1] => [6,4,2,1] => [4,2,1] => 1001010 => 0
[7,5,4,2,1] => [5,4,2,1] => [4,2,1] => 1001010 => 0
[7,6,3,2,1] => [6,3,2,1] => [3,2,1] => 101010 => 0
[6,6,3,2,1] => [6,3,2,1] => [3,2,1] => 101010 => 0
[7,6,5,4] => [6,5,4] => [5,4] => 1010000 => 0
[6,5,5,4] => [5,5,4] => [5,4] => 1010000 => 0
[7,6,5,3] => [6,5,3] => [5,3] => 1001000 => 0
[7,6,4,3] => [6,4,3] => [4,3] => 101000 => 0
[7,5,4,3] => [5,4,3] => [4,3] => 101000 => 0
[7,6,5,2] => [6,5,2] => [5,2] => 1000100 => 0
[7,6,5] => [6,5] => [5] => 100000 => 0
[2,2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => 111111100 => 0
[3,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => 1111000 => 0
[3,3,3,3,3,3,3,3] => [3,3,3,3,3,3,3] => [3,3,3,3,3,3] => 111111000 => 0
[3,3,3,3,3,3,1] => [3,3,3,3,3,1] => [3,3,3,3,1] => 11110010 => 0
[3,3,3,3,3,3,3] => [3,3,3,3,3,3] => [3,3,3,3,3] => 11111000 => 0
[3,3,3,3,3,2,2] => [3,3,3,3,2,2] => [3,3,3,2,2] => 11101100 => 0
[4,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => 1111000 => 0
[4,4,4,4,4] => [4,4,4,4] => [4,4,4] => 1110000 => 0
[4,4,4,3,3,3] => [4,4,3,3,3] => [4,3,3,3] => 10111000 => 0
[4,4,4,4,4,4] => [4,4,4,4,4] => [4,4,4,4] => 11110000 => 0
[5,5,5,5] => [5,5,5] => [5,5] => 1100000 => 0
[6,6,6,6] => [6,6,6] => [6,6] => 11000000 => 0
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0
[6,6,6] => [6,6] => [6] => 1000000 => 0
[7,6,6] => [6,6] => [6] => 1000000 => 0
[10,4,4] => [4,4] => [4] => 10000 => 0
[6,6,6,6,6] => [6,6,6,6] => [6,6,6] => 111000000 => 0
[11,7,3] => [7,3] => [3] => 1000 => 0
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0
[9,6,3] => [6,3] => [3] => 1000 => 0
[8,6,4,2] => [6,4,2] => [4,2] => 100100 => 0
[8,6,4] => [6,4] => [4] => 10000 => 0
[10,6,4] => [6,4] => [4] => 10000 => 0
[8,7,6] => [7,6] => [6] => 1000000 => 0
[9,8,7] => [8,7] => [7] => 10000000 => 0
[5,5,5,5,5,5] => [5,5,5,5,5] => [5,5,5,5] => 111100000 => 0
[15,5,5] => [5,5] => [5] => 100000 => 0
[7,7,7,7] => [7,7,7] => [7,7] => 110000000 => 0
[7,7,7] => [7,7] => [7] => 10000000 => 0
[11,7,5,1] => [7,5,1] => [5,1] => 1000010 => 0
[9,7,5,3,1] => [7,5,3,1] => [5,3,1] => 10010010 => 0
[8,7,4,4,3,2,1] => [7,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 0
[9,6,4] => [6,4] => [4] => 10000 => 0
[10,7,3] => [7,3] => [3] => 1000 => 0
[8,5,4,2] => [5,4,2] => [4,2] => 100100 => 0
[9,6,5,3] => [6,5,3] => [5,3] => 1001000 => 0
[10,7,5,3] => [7,5,3] => [5,3] => 1001000 => 0
[9,6,4,3] => [6,4,3] => [4,3] => 101000 => 0
[9,7,4] => [7,4] => [4] => 10000 => 0
[9,7,5,4,1] => [7,5,4,1] => [5,4,1] => 10100010 => 0
[8,6,5,3,1] => [6,5,3,1] => [5,3,1] => 10010010 => 0
[10,8,6,4,2] => [8,6,4,2] => [6,4,2] => 100100100 => 0
[8,5,5,1] => [5,5,1] => [5,1] => 1000010 => 0
[9,5,5,1] => [5,5,1] => [5,1] => 1000010 => 0
[9,7,5,3] => [7,5,3] => [5,3] => 1001000 => 0
[5,5,5,5,5] => [5,5,5,5] => [5,5,5] => 11100000 => 0
[8,8,8] => [8,8] => [8] => 100000000 => 0
[4,4,4,4,4,4,4] => [4,4,4,4,4,4] => [4,4,4,4,4] => 111110000 => 0
[7,7,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => 11110 => 0
[8,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[8,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0
[5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 0
[8,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 101010100 => 0
[5,4,4,4,4,2,1] => [4,4,4,4,2,1] => [4,4,4,2,1] => 111001010 => 0
[5,4,3,3,3,3,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => 11110010 => 0
[5,4,3,2,2,2,2] => [4,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 0
[6,5,5,5] => [5,5,5] => [5,5] => 1100000 => 0
[5,4,4,4,4] => [4,4,4,4] => [4,4,4] => 1110000 => 0
[8,7,6,5] => [7,6,5] => [6,5] => 10100000 => 0
[8,7,6,5,4] => [7,6,5,4] => [6,5,4] => 101010000 => 0
[8,7,5] => [7,5] => [5] => 100000 => 0
[9,8,7,6] => [8,7,6] => [7,6] => 101000000 => 0
[8,7,6,4] => [7,6,4] => [6,4] => 10010000 => 0
[8,7,6,5,3] => [7,6,5,3] => [6,5,3] => 101001000 => 0
[4,4,4,4,4,1] => [4,4,4,4,1] => [4,4,4,1] => 11100010 => 0
[5,5,5,5,1] => [5,5,5,1] => [5,5,1] => 11000010 => 0
[6,6,6,1] => [6,6,1] => [6,1] => 10000010 => 0
[6,6,6,1,1] => [6,6,1,1] => [6,1,1] => 100000110 => 0
[7,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => 10101010 => 0
[6,5,4,3,2,2,2] => [5,4,3,2,2,2] => [4,3,2,2,2] => 101011100 => 0
[8,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 101010110 => 0
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Description
The length of the longest Yamanouchi prefix of a binary word.
This is the largest index $i$ such that in each of the prefixes $w_1$, $w_1w_2$, $w_1w_2\dots w_i$ the number of zeros is greater than or equal to the number of ones.
This is the largest index $i$ such that in each of the prefixes $w_1$, $w_1w_2$, $w_1w_2\dots w_i$ the number of zeros is greater than or equal to the number of ones.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
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