Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St000877: Binary words ⟶ ℤ
Values
[1,1] => [1] => [1,0,1,0] => 1010 => 0
[2,1] => [1] => [1,0,1,0] => 1010 => 0
[1,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[3,1] => [1] => [1,0,1,0] => 1010 => 0
[2,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[2,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[1,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[4,1] => [1] => [1,0,1,0] => 1010 => 0
[3,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[3,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[2,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[2,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[1,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[5,1] => [1] => [1,0,1,0] => 1010 => 0
[4,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[4,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[3,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[3,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[3,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[2,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[2,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[6,1] => [1] => [1,0,1,0] => 1010 => 0
[5,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[5,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[4,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[4,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[4,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[3,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[3,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[2,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[7,1] => [1] => [1,0,1,0] => 1010 => 0
[6,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[6,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[5,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[5,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[5,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[4,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[4,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[4,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[3,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
[3,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[3,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[2,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[2,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[8,1] => [1] => [1,0,1,0] => 1010 => 0
[7,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[7,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[6,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[6,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[6,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[5,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[5,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[5,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[5,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[4,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0
[4,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
[4,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[4,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[3,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0
[3,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 0
[3,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0
[3,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[3,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[2,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0
[2,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 0
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 0
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 0
[9,1] => [1] => [1,0,1,0] => 1010 => 0
[8,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[8,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[7,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[7,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[7,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[6,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[6,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[6,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[6,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[5,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 0
[5,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0
[5,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
>>> Load all 985 entries. <<<[5,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[5,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[4,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0
[4,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0
[4,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0
[4,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 0
[4,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0
[4,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[4,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[3,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0
[3,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0
[3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 0
[3,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0
[3,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 0
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 0
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[2,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 0
[2,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 0
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 0
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 0
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 0
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 0
[10,1] => [1] => [1,0,1,0] => 1010 => 0
[9,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[9,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[8,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[8,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[8,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[7,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[7,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[7,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[7,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[6,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 0
[6,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0
[6,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
[6,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[6,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[5,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 0
[5,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0
[5,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0
[5,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0
[5,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 0
[5,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0
[5,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[5,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[4,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0
[4,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0
[4,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0
[4,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0
[4,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0
[4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 0
[4,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0
[4,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 0
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 0
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[3,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0
[3,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0
[3,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0
[3,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 0
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 0
[3,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 0
[3,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 0
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 0
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 0
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 0
[2,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 0
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 0
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 0
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 0
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 0
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 0
[11,1] => [1] => [1,0,1,0] => 1010 => 0
[10,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[10,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[9,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[9,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[9,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[8,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[8,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[8,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[8,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[7,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 0
[7,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0
[7,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
[7,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[7,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[6,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 0
[6,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 0
[6,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0
[6,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0
[6,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0
[6,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 0
[6,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0
[6,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[6,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[5,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 0
[5,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 0
[5,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0
[5,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0
[5,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0
[5,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0
[5,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0
[5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 0
[5,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0
[5,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 0
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 0
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[4,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 0
[4,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0
[4,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0
[4,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 0
[4,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0
[4,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0
[4,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0
[4,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 0
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 0
[4,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 0
[4,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 0
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 0
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 0
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 0
[3,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 0
[3,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0
[3,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 0
[3,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 0
[3,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 0
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 0
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 0
[3,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 0
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 0
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 0
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 0
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 0
[2,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 0
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 0
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 0
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => 0
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 10111111110100000000 => 0
[2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 0
[12,1] => [1] => [1,0,1,0] => 1010 => 0
[11,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[11,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[10,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[10,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[10,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[9,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[9,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[9,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[9,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[8,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 0
[8,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0
[8,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
[8,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[8,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[7,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 0
[7,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 0
[7,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0
[7,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0
[7,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0
[7,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 0
[7,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0
[7,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[7,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[6,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 0
[6,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 0
[6,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 0
[6,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0
[6,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0
[6,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0
[6,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0
[6,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0
[6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 0
[6,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0
[6,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 0
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 0
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[5,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 0
[5,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 0
[5,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 0
[5,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 0
[5,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0
[5,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0
[5,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 0
[5,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0
[5,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0
[5,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0
[5,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 0
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 0
[5,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 0
[5,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 0
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 0
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 0
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 0
[4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 0
[4,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0
[4,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0
[4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0
[4,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 0
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 0
[4,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 0
[4,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0
[4,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 0
[4,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 0
[4,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 0
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 0
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 0
[4,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 0
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 0
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 0
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 0
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 0
[3,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 0
[3,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 0
[3,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 0
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 0
[3,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 0
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 0
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 0
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 101111111001000000 => 0
[3,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 0
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 0
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 0
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => 0
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 10111111110100000000 => 0
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 0
[13,1] => [1] => [1,0,1,0] => 1010 => 0
[12,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[12,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[11,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[11,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[11,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[10,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[10,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[10,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[10,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[9,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 0
[9,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0
[9,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
[9,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[9,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[8,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 0
[8,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 0
[8,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0
[8,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0
[8,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0
[8,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 0
[8,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0
[8,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[8,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[7,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 0
[7,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 0
[7,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 0
[7,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 0
[7,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0
[7,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0
[7,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0
[7,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0
[7,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0
[7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 0
[7,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0
[7,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 0
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 0
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[6,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 0
[6,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 0
[6,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 0
[6,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 0
[6,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 0
[6,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 0
[6,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0
[6,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0
[6,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 0
[6,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0
[6,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0
[6,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0
[6,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 0
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 0
[6,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 0
[6,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 0
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 0
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 0
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 0
[5,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 0
[5,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 0
[5,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 0
[5,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 0
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 0
[5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 0
[5,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0
[5,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0
[5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0
[5,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 0
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 0
[5,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 0
[5,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0
[5,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 0
[5,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 0
[5,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 0
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 0
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 0
[5,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 0
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 0
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 0
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 0
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 0
[4,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 0
[4,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 0
[4,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 0
[4,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0
[4,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 0
[4,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 0
[4,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 0
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 0
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 0
[4,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 0
[4,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 0
[4,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 0
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 0
[4,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 0
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 0
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 0
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 101111111001000000 => 0
[4,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 0
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 0
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 0
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => 0
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 10111111110100000000 => 0
[4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 0
[3,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 0
[3,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 0
[3,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 0
[14,1] => [1] => [1,0,1,0] => 1010 => 0
[13,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[13,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[12,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[12,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[12,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[11,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[11,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[11,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[11,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[10,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 0
[10,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0
[10,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
[10,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[10,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[9,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 0
[9,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 0
[9,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0
[9,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0
[9,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0
[9,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 0
[9,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0
[9,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[9,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[8,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 0
[8,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 0
[8,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 0
[8,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 0
[8,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0
[8,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0
[8,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0
[8,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0
[8,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0
[8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 0
[8,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0
[8,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 0
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 0
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[7,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 0
[7,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 0
[7,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 0
[7,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 0
[7,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 0
[7,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 0
[7,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 0
[7,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0
[7,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0
[7,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 0
[7,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0
[7,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0
[7,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0
[7,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 0
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 0
[7,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 0
[7,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 0
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 0
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 0
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 0
[6,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 0
[6,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 0
[6,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 0
[6,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 0
[6,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 0
[6,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 0
[6,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 0
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 0
[6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 0
[6,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0
[6,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0
[6,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0
[6,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 0
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 0
[6,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 0
[6,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0
[6,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 0
[6,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 0
[6,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 0
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 0
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 0
[6,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 0
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 0
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 0
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 0
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 0
[5,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 0
[5,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 0
[5,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 0
[5,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 0
[5,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 0
[5,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 0
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 0
[5,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 0
[5,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 0
[5,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 0
[5,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0
[5,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 0
[5,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 0
[5,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 0
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 0
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 0
[5,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 0
[5,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 0
[5,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 0
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 0
[5,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 0
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 0
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 0
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 101111111001000000 => 0
[5,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 0
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 0
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 0
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => 0
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 10111111110100000000 => 0
[5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 0
[4,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 0
[4,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 0
[4,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 0
[4,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 0
[4,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 0
[4,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 0
[4,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 0
[4,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 0
[4,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 0
[4,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 0
[3,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 0
[15,1] => [1] => [1,0,1,0] => 1010 => 0
[14,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[14,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[13,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[13,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[13,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[12,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[12,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[12,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[12,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[11,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 0
[11,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0
[11,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
[11,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[11,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[10,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 0
[10,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 0
[10,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0
[10,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0
[10,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0
[10,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 0
[10,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0
[10,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[10,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[9,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 0
[9,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 0
[9,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 0
[9,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 0
[9,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0
[9,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0
[9,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0
[9,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0
[9,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0
[9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 0
[9,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0
[9,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 0
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 0
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[8,8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 0
[8,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 0
[8,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 0
[8,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 0
[8,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 0
[8,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 0
[8,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 0
[8,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 0
[8,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0
[8,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0
[8,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 0
[8,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0
[8,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0
[8,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0
[8,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 0
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 0
[8,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 0
[8,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 0
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 0
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 0
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 0
[7,7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 0
[7,7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 0
[7,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 0
[7,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 0
[7,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 0
[7,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 0
[7,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 0
[7,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 0
[7,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 0
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 0
[7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 0
[7,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0
[7,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0
[7,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0
[7,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 0
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 0
[7,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 0
[7,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0
[7,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 0
[7,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 0
[7,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 0
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 0
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 0
[7,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 0
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 0
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 0
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 0
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 0
[6,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 0
[6,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 0
[6,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 0
[6,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 0
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 0
[6,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 0
[6,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 0
[6,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 0
[6,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 0
[6,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 0
[6,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 0
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 0
[6,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 0
[6,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 0
[6,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 0
[6,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0
[6,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 0
[6,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 0
[6,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 0
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 0
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 0
[6,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 0
[6,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 0
[6,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 0
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 0
[6,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 0
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 0
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 0
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 101111111001000000 => 0
[6,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 0
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 0
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 0
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => 0
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 10111111110100000000 => 0
[6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 0
[5,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 0
[5,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 0
[5,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => 0
[5,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 0
[5,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 0
[5,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 0
[5,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 0
[5,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 0
[5,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 0
[5,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 0
[5,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 0
[5,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 0
[5,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 0
[5,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 0
[5,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 0
[5,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 0
[5,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 0
[4,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 0
[4,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 0
[4,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 0
[4,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 0
[4,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 0
[4,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 0
[4,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 0
[16,1] => [1] => [1,0,1,0] => 1010 => 0
[15,2] => [2] => [1,1,0,0,1,0] => 110010 => 0
[15,1,1] => [1,1] => [1,0,1,1,0,0] => 101100 => 0
[14,3] => [3] => [1,1,1,0,0,0,1,0] => 11100010 => 0
[14,2,1] => [2,1] => [1,0,1,0,1,0] => 101010 => 0
[14,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 0
[13,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0
[13,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 0
[13,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 0
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 0
[13,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0
[12,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 0
[12,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0
[12,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 0
[12,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 0
[12,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 0
[12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 0
[11,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 0
[11,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 0
[11,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0
[11,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0
[11,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0
[11,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 0
[11,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0
[11,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0
[11,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 0
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 0
[10,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 0
[10,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 0
[10,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 0
[10,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 0
[10,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0
[10,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0
[10,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0
[10,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0
[10,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0
[10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 0
[10,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0
[10,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 0
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 0
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 0
[9,8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 0
[9,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 0
[9,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 0
[9,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 0
[9,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 0
[9,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 0
[9,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 0
[9,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 0
[9,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0
[9,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0
[9,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 0
[9,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0
[9,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0
[9,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0
[9,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 0
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 0
[9,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 0
[9,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 0
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 0
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 0
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 0
[8,8,1] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 111111101000000010 => 0
[8,7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 0
[8,7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 0
[8,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 0
[8,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 0
[8,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 0
[8,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 0
[8,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 0
[8,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 0
[8,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 0
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 0
[8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 0
[8,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0
[8,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0
[8,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0
[8,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 0
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 0
[8,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 0
[8,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0
[8,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 0
[8,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 0
[8,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 0
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 0
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 0
[8,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 0
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 0
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 0
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 0
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 0
[7,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 0
[7,7,2,1] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 0
[7,7,1,1,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 0
[7,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 0
[7,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 0
[7,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 0
[7,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 0
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 0
[7,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 0
[7,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 0
[7,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 0
[7,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 0
[7,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 0
[7,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 0
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 0
[7,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 0
[7,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 0
[7,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 0
[7,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0
[7,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 0
[7,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 0
[7,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 0
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 0
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 0
[7,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 0
[7,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 0
[7,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 0
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 0
[7,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 0
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 0
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 0
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 101111111001000000 => 0
[7,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 0
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 0
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 0
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => 0
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 10111111110100000000 => 0
[7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 0
[6,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 0
[6,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 0
[6,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => 0
[6,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 0
[6,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 0
[6,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 0
[6,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 0
[6,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 0
[6,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 0
[6,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 0
[6,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 0
[6,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 0
[6,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 0
[6,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 0
[6,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 0
[6,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 0
[6,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 0
[5,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 0
[5,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 0
[5,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 0
[5,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 0
[5,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 0
[5,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 0
[5,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 0
[5,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 0
[5,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 0
[5,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 0
[5,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 0
[5,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 0
[5,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 0
[5,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 0
[4,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 0
[4,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 0
[4,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 0
[4,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 0
[6,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 0
[5,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 0
[6,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 0
[5,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 0
[4,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 0
[6,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 0
[5,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 0
[6,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 0
[5,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 0
[6,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 0
[6,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 0
[5,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 0
[6,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 0
[5,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 0
[6,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 0
[5,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 0
[6,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 0
[6,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 0
[6,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 0
[5,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 0
[6,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 0
[5,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 0
[6,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 0
[5,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 0
[6,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 0
[6,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 0
[5,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 0
[6,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 0
[6,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 0
[6,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 0
[6,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 0
[5,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 0
[6,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 0
[5,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 0
[6,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 0
[5,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 0
[6,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 0
[6,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 0
[5,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 0
[6,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 0
[6,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 0
[6,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 0
[5,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 0
[6,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 0
[6,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 0
[6,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 0
[6,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 0
[7,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 0
[7,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 0
[7,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 0
[7,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 0
[7,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 0
[7,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 0
[7,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 0
[7,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 0
[7,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 0
[10,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 0
[10,10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1111111111000000000010 => 0
[11,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 0
[9,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 0
[8,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 0
[10,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 0
[15,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 0
[9,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 0
[10,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 0
[8,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 0
[9,9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => 0
[8,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 0
search for individual values
searching the database for the individual values of this statistic
Description
The depth of the binary word interpreted as a path.
This is the maximal value of the number of zeros minus the number of ones occurring in a prefix of the binary word, see [1, sec.9.1.2].
The number of binary words of length $n$ with depth $k$ is $\binom{n}{\lfloor\frac{(n+1) - (-1)^{n-k}(k+1)}{2}\rfloor}$, see [2].
This is the maximal value of the number of zeros minus the number of ones occurring in a prefix of the binary word, see [1, sec.9.1.2].
The number of binary words of length $n$ with depth $k$ is $\binom{n}{\lfloor\frac{(n+1) - (-1)^{n-k}(k+1)}{2}\rfloor}$, see [2].
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to binary word
Description
Return the Dyck word as binary word.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
searching the database
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