Identifier
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Images
[1,0] => [1] => 1 => [1,1]
[1,0,1,0] => [1,1] => 11 => [1,1,1]
[1,1,0,0] => [2] => 10 => [1,2]
[1,0,1,0,1,0] => [1,1,1] => 111 => [1,1,1,1]
[1,0,1,1,0,0] => [1,2] => 110 => [1,1,2]
[1,1,0,0,1,0] => [2,1] => 101 => [1,2,1]
[1,1,0,1,0,0] => [2,1] => 101 => [1,2,1]
[1,1,1,0,0,0] => [3] => 100 => [1,3]
[1,0,1,0,1,0,1,0] => [1,1,1,1] => 1111 => [1,1,1,1,1]
[1,0,1,0,1,1,0,0] => [1,1,2] => 1110 => [1,1,1,2]
[1,0,1,1,0,0,1,0] => [1,2,1] => 1101 => [1,1,2,1]
[1,0,1,1,0,1,0,0] => [1,2,1] => 1101 => [1,1,2,1]
[1,0,1,1,1,0,0,0] => [1,3] => 1100 => [1,1,3]
[1,1,0,0,1,0,1,0] => [2,1,1] => 1011 => [1,2,1,1]
[1,1,0,0,1,1,0,0] => [2,2] => 1010 => [1,2,2]
[1,1,0,1,0,0,1,0] => [2,1,1] => 1011 => [1,2,1,1]
[1,1,0,1,0,1,0,0] => [2,1,1] => 1011 => [1,2,1,1]
[1,1,0,1,1,0,0,0] => [2,2] => 1010 => [1,2,2]
[1,1,1,0,0,0,1,0] => [3,1] => 1001 => [1,3,1]
[1,1,1,0,0,1,0,0] => [3,1] => 1001 => [1,3,1]
[1,1,1,0,1,0,0,0] => [3,1] => 1001 => [1,3,1]
[1,1,1,1,0,0,0,0] => [4] => 1000 => [1,4]
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => 11111 => [1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => 11110 => [1,1,1,1,2]
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => 11101 => [1,1,1,2,1]
[1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => 11101 => [1,1,1,2,1]
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 11100 => [1,1,1,3]
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => 11011 => [1,1,2,1,1]
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => 11010 => [1,1,2,2]
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => 11011 => [1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => 11011 => [1,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0] => [1,2,2] => 11010 => [1,1,2,2]
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 11001 => [1,1,3,1]
[1,0,1,1,1,0,0,1,0,0] => [1,3,1] => 11001 => [1,1,3,1]
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => 11001 => [1,1,3,1]
[1,0,1,1,1,1,0,0,0,0] => [1,4] => 11000 => [1,1,4]
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => 10111 => [1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => 10110 => [1,2,1,2]
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 10101 => [1,2,2,1]
[1,1,0,0,1,1,0,1,0,0] => [2,2,1] => 10101 => [1,2,2,1]
[1,1,0,0,1,1,1,0,0,0] => [2,3] => 10100 => [1,2,3]
[1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => 10111 => [1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => 10110 => [1,2,1,2]
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => 10111 => [1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => 10111 => [1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => 10110 => [1,2,1,2]
[1,1,0,1,1,0,0,0,1,0] => [2,2,1] => 10101 => [1,2,2,1]
[1,1,0,1,1,0,0,1,0,0] => [2,2,1] => 10101 => [1,2,2,1]
[1,1,0,1,1,0,1,0,0,0] => [2,2,1] => 10101 => [1,2,2,1]
[1,1,0,1,1,1,0,0,0,0] => [2,3] => 10100 => [1,2,3]
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => 10011 => [1,3,1,1]
[1,1,1,0,0,0,1,1,0,0] => [3,2] => 10010 => [1,3,2]
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => 10011 => [1,3,1,1]
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => 10011 => [1,3,1,1]
[1,1,1,0,0,1,1,0,0,0] => [3,2] => 10010 => [1,3,2]
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => 10011 => [1,3,1,1]
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => 10011 => [1,3,1,1]
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => 10011 => [1,3,1,1]
[1,1,1,0,1,1,0,0,0,0] => [3,2] => 10010 => [1,3,2]
[1,1,1,1,0,0,0,0,1,0] => [4,1] => 10001 => [1,4,1]
[1,1,1,1,0,0,0,1,0,0] => [4,1] => 10001 => [1,4,1]
[1,1,1,1,0,0,1,0,0,0] => [4,1] => 10001 => [1,4,1]
[1,1,1,1,0,1,0,0,0,0] => [4,1] => 10001 => [1,4,1]
[1,1,1,1,1,0,0,0,0,0] => [5] => 10000 => [1,5]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => 111111 => [1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => 111110 => [1,1,1,1,1,2]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => 111101 => [1,1,1,1,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => 111101 => [1,1,1,1,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 111100 => [1,1,1,1,3]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => 111011 => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => 111010 => [1,1,1,2,2]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => 111011 => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => 111011 => [1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => 111010 => [1,1,1,2,2]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => 111001 => [1,1,1,3,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => 111001 => [1,1,1,3,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => 111001 => [1,1,1,3,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 111000 => [1,1,1,4]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => 110111 => [1,1,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => 110110 => [1,1,2,1,2]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => 110101 => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => 110101 => [1,1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => 110100 => [1,1,2,3]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => 110111 => [1,1,2,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => 110110 => [1,1,2,1,2]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => 110111 => [1,1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => 110111 => [1,1,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => 110110 => [1,1,2,1,2]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => 110101 => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => 110101 => [1,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => 110101 => [1,1,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => 110100 => [1,1,2,3]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => 110011 => [1,1,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => 110010 => [1,1,3,2]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => 110011 => [1,1,3,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => 110011 => [1,1,3,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => 110010 => [1,1,3,2]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => 110011 => [1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => 110011 => [1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => 110011 => [1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => 110010 => [1,1,3,2]
>>> Load all 5249 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => 110001 => [1,1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => 110001 => [1,1,4,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => 110001 => [1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => 110001 => [1,1,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 110000 => [1,1,5]
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => 101111 => [1,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => 101110 => [1,2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => 101101 => [1,2,1,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => 101101 => [1,2,1,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 101100 => [1,2,1,3]
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => 101011 => [1,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => 101010 => [1,2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => 101011 => [1,2,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => 101011 => [1,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => 101010 => [1,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => 101001 => [1,2,3,1]
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => 101001 => [1,2,3,1]
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => 101001 => [1,2,3,1]
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => 101000 => [1,2,4]
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => 101111 => [1,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => 101110 => [1,2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => 101101 => [1,2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => 101101 => [1,2,1,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => 101100 => [1,2,1,3]
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => 101111 => [1,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => 101110 => [1,2,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => 101111 => [1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => 101111 => [1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,2] => 101110 => [1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => 101101 => [1,2,1,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => 101101 => [1,2,1,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => 101101 => [1,2,1,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => 101100 => [1,2,1,3]
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => 101011 => [1,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => 101010 => [1,2,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => 101011 => [1,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,1] => 101011 => [1,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2] => 101010 => [1,2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => 101011 => [1,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,1] => 101011 => [1,2,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,1] => 101011 => [1,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2] => 101010 => [1,2,2,2]
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => 101001 => [1,2,3,1]
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => 101001 => [1,2,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => 101001 => [1,2,3,1]
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => 101001 => [1,2,3,1]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,4] => 101000 => [1,2,4]
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => 100110 => [1,3,1,2]
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => 100101 => [1,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => 100101 => [1,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => 100100 => [1,3,3]
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => 100110 => [1,3,1,2]
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => 100110 => [1,3,1,2]
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => 100101 => [1,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => 100101 => [1,3,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => 100101 => [1,3,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => 100100 => [1,3,3]
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => 100110 => [1,3,1,2]
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => 100110 => [1,3,1,2]
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => 100111 => [1,3,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => 100110 => [1,3,1,2]
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => 100101 => [1,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => 100101 => [1,3,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => 100101 => [1,3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => 100101 => [1,3,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => 100100 => [1,3,3]
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => 100010 => [1,4,2]
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,2] => 100010 => [1,4,2]
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,2] => 100010 => [1,4,2]
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => 100011 => [1,4,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,2] => 100010 => [1,4,2]
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => 100001 => [1,5,1]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => 100001 => [1,5,1]
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => 100001 => [1,5,1]
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => 100001 => [1,5,1]
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => 100001 => [1,5,1]
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => 100000 => [1,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => 1111111 => [1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => 1111110 => [1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => 1111101 => [1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,2,1] => 1111101 => [1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => 1111100 => [1,1,1,1,1,3]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => 1111011 => [1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => 1111010 => [1,1,1,1,2,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => 1111011 => [1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => 1111011 => [1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,2,2] => 1111010 => [1,1,1,1,2,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => 1111001 => [1,1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,3,1] => 1111001 => [1,1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,3,1] => 1111001 => [1,1,1,1,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => 1111000 => [1,1,1,1,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => 1110111 => [1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => 1110110 => [1,1,1,2,1,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => 1110101 => [1,1,1,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,2,1] => 1110101 => [1,1,1,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => 1110100 => [1,1,1,2,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1] => 1110111 => [1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,2,1,2] => 1110110 => [1,1,1,2,1,2]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1] => 1110111 => [1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1] => 1110111 => [1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,2,1,2] => 1110110 => [1,1,1,2,1,2]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,2,2,1] => 1110101 => [1,1,1,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,2,2,1] => 1110101 => [1,1,1,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1] => 1110101 => [1,1,1,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,2,3] => 1110100 => [1,1,1,2,3]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => 1110011 => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => 1110010 => [1,1,1,3,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => 1110011 => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => 1110011 => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => 1110010 => [1,1,1,3,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => 1110011 => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => 1110011 => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => 1110011 => [1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => 1110010 => [1,1,1,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => 1110001 => [1,1,1,4,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,4,1] => 1110001 => [1,1,1,4,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => 1110001 => [1,1,1,4,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => 1110001 => [1,1,1,4,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => 1110000 => [1,1,1,5]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 1101111 => [1,1,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => 1101110 => [1,1,2,1,1,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => 1101101 => [1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,2,1] => 1101101 => [1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => 1101100 => [1,1,2,1,3]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => 1101011 => [1,1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => 1101010 => [1,1,2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,2,1,1] => 1101011 => [1,1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,1] => 1101011 => [1,1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2] => 1101010 => [1,1,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => 1101001 => [1,1,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,3,1] => 1101001 => [1,1,2,3,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => 1101001 => [1,1,2,3,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => 1101000 => [1,1,2,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 1101111 => [1,1,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,2] => 1101110 => [1,1,2,1,1,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => 1101101 => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => 1101101 => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => 1101100 => [1,1,2,1,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1] => 1101111 => [1,1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,2] => 1101110 => [1,1,2,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1] => 1101111 => [1,1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1] => 1101111 => [1,1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,2] => 1101110 => [1,1,2,1,1,2]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => 1101101 => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => 1101101 => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => 1101101 => [1,1,2,1,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => 1101100 => [1,1,2,1,3]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,2,1,1] => 1101011 => [1,1,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2] => 1101010 => [1,1,2,2,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,2,1,1] => 1101011 => [1,1,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,2,1,1] => 1101011 => [1,1,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2] => 1101010 => [1,1,2,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,2,1,1] => 1101011 => [1,1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,2,1,1] => 1101011 => [1,1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,2,1,1] => 1101011 => [1,1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2] => 1101010 => [1,1,2,2,2]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => 1101001 => [1,1,2,3,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => 1101001 => [1,1,2,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => 1101001 => [1,1,2,3,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => 1101001 => [1,1,2,3,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4] => 1101000 => [1,1,2,4]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => 1100110 => [1,1,3,1,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => 1100101 => [1,1,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => 1100101 => [1,1,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => 1100100 => [1,1,3,3]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => 1100110 => [1,1,3,1,2]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => 1100110 => [1,1,3,1,2]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => 1100101 => [1,1,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => 1100101 => [1,1,3,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => 1100101 => [1,1,3,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => 1100100 => [1,1,3,3]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => 1100110 => [1,1,3,1,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => 1100110 => [1,1,3,1,2]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1] => 1100111 => [1,1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => 1100110 => [1,1,3,1,2]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => 1100101 => [1,1,3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => 1100101 => [1,1,3,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => 1100101 => [1,1,3,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => 1100101 => [1,1,3,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => 1100100 => [1,1,3,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => 1100010 => [1,1,4,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => 1100010 => [1,1,4,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => 1100010 => [1,1,4,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => 1100011 => [1,1,4,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => 1100010 => [1,1,4,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => 1100001 => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => 1100001 => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => 1100001 => [1,1,5,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => 1100001 => [1,1,5,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => 1100001 => [1,1,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => 1100000 => [1,1,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1011111 => [1,2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 1011110 => [1,2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1011101 => [1,2,1,1,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => 1011101 => [1,2,1,1,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 1011100 => [1,2,1,1,3]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 1011010 => [1,2,1,2,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 1011010 => [1,2,1,2,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => 1011000 => [1,2,1,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => 1010110 => [1,2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => 1010100 => [1,2,2,3]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => 1010110 => [1,2,2,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => 1010110 => [1,2,2,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => 1010100 => [1,2,2,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => 1010010 => [1,2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => 1010010 => [1,2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => 1010010 => [1,2,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => 1010001 => [1,2,4,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => 1010001 => [1,2,4,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => 1010001 => [1,2,4,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => 1010001 => [1,2,4,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => 1010000 => [1,2,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1011111 => [1,2,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 1011110 => [1,2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1011101 => [1,2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => 1011101 => [1,2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 1011100 => [1,2,1,1,3]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 1011010 => [1,2,1,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 1011010 => [1,2,1,2,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => 1011000 => [1,2,1,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1011111 => [1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => 1011110 => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1011101 => [1,2,1,1,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => 1011101 => [1,2,1,1,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => 1011100 => [1,2,1,1,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => 1011111 => [1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => 1011110 => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => 1011111 => [1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1] => 1011111 => [1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,2] => 1011110 => [1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => 1011101 => [1,2,1,1,2,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,2,1] => 1011101 => [1,2,1,1,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,2,1] => 1011101 => [1,2,1,1,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,3] => 1011100 => [1,2,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => 1011010 => [1,2,1,2,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,2,2] => 1011010 => [1,2,1,2,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,1] => 1011011 => [1,2,1,2,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2] => 1011010 => [1,2,1,2,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,3,1] => 1011001 => [1,2,1,3,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4] => 1011000 => [1,2,1,4]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => 1010110 => [1,2,2,1,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => 1010100 => [1,2,2,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => 1010110 => [1,2,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,1,2] => 1010110 => [1,2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,3] => 1010100 => [1,2,2,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => 1010110 => [1,2,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,2,1,2] => 1010110 => [1,2,2,1,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1] => 1010111 => [1,2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1,2] => 1010110 => [1,2,2,1,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,1] => 1010101 => [1,2,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,3] => 1010100 => [1,2,2,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => 1010010 => [1,2,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,2] => 1010010 => [1,2,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,2] => 1010010 => [1,2,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,1] => 1010011 => [1,2,3,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,2] => 1010010 => [1,2,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => 1010001 => [1,2,4,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1] => 1010001 => [1,2,4,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1] => 1010001 => [1,2,4,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1] => 1010001 => [1,2,4,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,1] => 1010001 => [1,2,4,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,5] => 1010000 => [1,2,5]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 1001100 => [1,3,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => 1001010 => [1,3,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => 1001010 => [1,3,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => 1001000 => [1,3,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => 1001100 => [1,3,1,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => 1001100 => [1,3,1,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => 1001010 => [1,3,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2] => 1001010 => [1,3,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2] => 1001010 => [1,3,2,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4] => 1001000 => [1,3,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => 1001100 => [1,3,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => 1001100 => [1,3,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => 1001111 => [1,3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,2] => 1001110 => [1,3,1,1,2]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,2,1] => 1001101 => [1,3,1,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => 1001100 => [1,3,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => 1001010 => [1,3,2,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,2] => 1001010 => [1,3,2,2]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2] => 1001010 => [1,3,2,2]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 1001011 => [1,3,2,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2] => 1001010 => [1,3,2,2]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,3,1] => 1001001 => [1,3,3,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4] => 1001000 => [1,3,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => 1000100 => [1,4,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3] => 1000100 => [1,4,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3] => 1000100 => [1,4,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1] => 1000111 => [1,4,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,1,2] => 1000110 => [1,4,1,2]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,1] => 1000101 => [1,4,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,3] => 1000100 => [1,4,3]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => 1000010 => [1,5,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,2] => 1000010 => [1,5,2]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,2] => 1000010 => [1,5,2]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,2] => 1000010 => [1,5,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => 1000011 => [1,5,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,2] => 1000010 => [1,5,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => 1000001 => [1,6,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1] => 1000001 => [1,6,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1] => 1000001 => [1,6,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1] => 1000001 => [1,6,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1] => 1000001 => [1,6,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,1] => 1000001 => [1,6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => 1000000 => [1,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => 11111111 => [1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => 11111110 => [1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => 11111101 => [1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,2,1] => 11111101 => [1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => 11111100 => [1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => 11111011 => [1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => 11111010 => [1,1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1] => 11111011 => [1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1] => 11111011 => [1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,2,2] => 11111010 => [1,1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => 11111001 => [1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,3,1] => 11111001 => [1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,3,1] => 11111001 => [1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => 11111000 => [1,1,1,1,1,4]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => 11110111 => [1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => 11110110 => [1,1,1,1,2,1,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => 11110101 => [1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,2,1] => 11110101 => [1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => 11110100 => [1,1,1,1,2,3]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1] => 11110111 => [1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,2,1,2] => 11110110 => [1,1,1,1,2,1,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,2,1,1,1] => 11110111 => [1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1] => 11110111 => [1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,2] => 11110110 => [1,1,1,1,2,1,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,2,2,1] => 11110101 => [1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,2,2,1] => 11110101 => [1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,2,2,1] => 11110101 => [1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,2,3] => 11110100 => [1,1,1,1,2,3]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => 11110011 => [1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => 11110010 => [1,1,1,1,3,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,3,1,1] => 11110011 => [1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1] => 11110011 => [1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,3,2] => 11110010 => [1,1,1,1,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1] => 11110011 => [1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1] => 11110011 => [1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1] => 11110011 => [1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,3,2] => 11110010 => [1,1,1,1,3,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => 11110001 => [1,1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,4,1] => 11110001 => [1,1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,4,1] => 11110001 => [1,1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,4,1] => 11110001 => [1,1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => 11110000 => [1,1,1,1,5]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 11101111 => [1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 11101110 => [1,1,1,2,1,1,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 11101101 => [1,1,1,2,1,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 11101101 => [1,1,1,2,1,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => 11101100 => [1,1,1,2,1,3]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => 11101011 => [1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => 11101010 => [1,1,1,2,2,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,2,1,1] => 11101011 => [1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,2,1,1] => 11101011 => [1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,2,2] => 11101010 => [1,1,1,2,2,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => 11101001 => [1,1,1,2,3,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,3,1] => 11101001 => [1,1,1,2,3,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,3,1] => 11101001 => [1,1,1,2,3,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => 11101000 => [1,1,1,2,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 11101111 => [1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 11101110 => [1,1,1,2,1,1,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 11101101 => [1,1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 11101101 => [1,1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,2,1,3] => 11101100 => [1,1,1,2,1,3]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1] => 11101111 => [1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,2,1,1,2] => 11101110 => [1,1,1,2,1,1,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1] => 11101111 => [1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1] => 11101111 => [1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,2] => 11101110 => [1,1,1,2,1,1,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,2,1,2,1] => 11101101 => [1,1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,2,1,2,1] => 11101101 => [1,1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,2,1] => 11101101 => [1,1,1,2,1,2,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,2,1,3] => 11101100 => [1,1,1,2,1,3]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,2,2,1,1] => 11101011 => [1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,2,2] => 11101010 => [1,1,1,2,2,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,2,2,1,1] => 11101011 => [1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,2,2,1,1] => 11101011 => [1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,2,2,2] => 11101010 => [1,1,1,2,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,2,2,1,1] => 11101011 => [1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,2,2,1,1] => 11101011 => [1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1] => 11101011 => [1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,2,2,2] => 11101010 => [1,1,1,2,2,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,2,3,1] => 11101001 => [1,1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,3,1] => 11101001 => [1,1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,2,3,1] => 11101001 => [1,1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,3,1] => 11101001 => [1,1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,2,4] => 11101000 => [1,1,1,2,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => 11100110 => [1,1,1,3,1,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 11100101 => [1,1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,2,1] => 11100101 => [1,1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => 11100100 => [1,1,1,3,3]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,2] => 11100110 => [1,1,1,3,1,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,3,1,2] => 11100110 => [1,1,1,3,1,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,3,2,1] => 11100101 => [1,1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,3,2,1] => 11100101 => [1,1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,3,2,1] => 11100101 => [1,1,1,3,2,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,3,3] => 11100100 => [1,1,1,3,3]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,3,1,2] => 11100110 => [1,1,1,3,1,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,3,1,2] => 11100110 => [1,1,1,3,1,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1] => 11100111 => [1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,2] => 11100110 => [1,1,1,3,1,2]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,3,2,1] => 11100101 => [1,1,1,3,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,3,2,1] => 11100101 => [1,1,1,3,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,3,2,1] => 11100101 => [1,1,1,3,2,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,3,2,1] => 11100101 => [1,1,1,3,2,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,3,3] => 11100100 => [1,1,1,3,3]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => 11100010 => [1,1,1,4,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,4,2] => 11100010 => [1,1,1,4,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,4,2] => 11100010 => [1,1,1,4,2]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,4,1,1] => 11100011 => [1,1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,4,2] => 11100010 => [1,1,1,4,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => 11100001 => [1,1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,5,1] => 11100001 => [1,1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,5,1] => 11100001 => [1,1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,5,1] => 11100001 => [1,1,1,5,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,5,1] => 11100001 => [1,1,1,5,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => 11100000 => [1,1,1,6]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => [1,1,2,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 11011110 => [1,1,2,1,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 11011101 => [1,1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 11011101 => [1,1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 11011100 => [1,1,2,1,1,3]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 11011010 => [1,1,2,1,2,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 11011010 => [1,1,2,1,2,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 11011000 => [1,1,2,1,4]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => [1,1,2,2,1,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => 11010100 => [1,1,2,2,3]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => [1,1,2,2,1,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => 11010110 => [1,1,2,2,1,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,2,3] => 11010100 => [1,1,2,2,3]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => 11010010 => [1,1,2,3,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,2] => 11010010 => [1,1,2,3,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,2] => 11010010 => [1,1,2,3,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => 11010001 => [1,1,2,4,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,1] => 11010001 => [1,1,2,4,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,1] => 11010001 => [1,1,2,4,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,1] => 11010001 => [1,1,2,4,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => 11010000 => [1,1,2,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => [1,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 11011110 => [1,1,2,1,1,1,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 11011101 => [1,1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 11011101 => [1,1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 11011100 => [1,1,2,1,1,3]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 11011010 => [1,1,2,1,2,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 11011010 => [1,1,2,1,2,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 11011000 => [1,1,2,1,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => [1,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 11011110 => [1,1,2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 11011101 => [1,1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 11011101 => [1,1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,3] => 11011100 => [1,1,2,1,1,3]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => [1,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,2] => 11011110 => [1,1,2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1] => 11011111 => [1,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1] => 11011111 => [1,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,2] => 11011110 => [1,1,2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,2,1] => 11011101 => [1,1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,2,1] => 11011101 => [1,1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,2,1] => 11011101 => [1,1,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,3] => 11011100 => [1,1,2,1,1,3]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,1,2,2] => 11011010 => [1,1,2,1,2,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,2,2] => 11011010 => [1,1,2,1,2,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,2,1,1] => 11011011 => [1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,2,1,2,2] => 11011010 => [1,1,2,1,2,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => 11011001 => [1,1,2,1,3,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,1,4] => 11011000 => [1,1,2,1,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => [1,1,2,2,1,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,2,2,3] => 11010100 => [1,1,2,2,3]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => [1,1,2,2,1,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => 11010110 => [1,1,2,2,1,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,2,2,3] => 11010100 => [1,1,2,2,3]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,2,2,1,2] => 11010110 => [1,1,2,2,1,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,2,2,1,2] => 11010110 => [1,1,2,2,1,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1] => 11010111 => [1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,2] => 11010110 => [1,1,2,2,1,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,2,2,2,1] => 11010101 => [1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,2,2,3] => 11010100 => [1,1,2,2,3]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,2] => 11010010 => [1,1,2,3,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,2,3,2] => 11010010 => [1,1,2,3,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2] => 11010010 => [1,1,2,3,2]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1] => 11010011 => [1,1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => 11010010 => [1,1,2,3,2]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,1] => 11010001 => [1,1,2,4,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,2,4,1] => 11010001 => [1,1,2,4,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,2,4,1] => 11010001 => [1,1,2,4,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,2,4,1] => 11010001 => [1,1,2,4,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,1] => 11010001 => [1,1,2,4,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,5] => 11010000 => [1,1,2,5]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 11001100 => [1,1,3,1,3]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => 11001010 => [1,1,3,2,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,2,2] => 11001010 => [1,1,3,2,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => 11001000 => [1,1,3,4]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,3,1,3] => 11001100 => [1,1,3,1,3]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,1,3] => 11001100 => [1,1,3,1,3]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,2,2] => 11001010 => [1,1,3,2,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2] => 11001010 => [1,1,3,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,2,2] => 11001010 => [1,1,3,2,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,4] => 11001000 => [1,1,3,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,3,1,3] => 11001100 => [1,1,3,1,3]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,3,1,3] => 11001100 => [1,1,3,1,3]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1] => 11001111 => [1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,2] => 11001110 => [1,1,3,1,1,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => 11001101 => [1,1,3,1,2,1]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,1,3] => 11001100 => [1,1,3,1,3]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,2,2] => 11001010 => [1,1,3,2,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,2,2] => 11001010 => [1,1,3,2,2]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,2,2] => 11001010 => [1,1,3,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1] => 11001011 => [1,1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => 11001010 => [1,1,3,2,2]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,3,1] => 11001001 => [1,1,3,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4] => 11001000 => [1,1,3,4]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => 11000100 => [1,1,4,3]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,3] => 11000100 => [1,1,4,3]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => 11000100 => [1,1,4,3]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1] => 11000111 => [1,1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,2] => 11000110 => [1,1,4,1,2]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,2,1] => 11000101 => [1,1,4,2,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => 11000100 => [1,1,4,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => 11000010 => [1,1,5,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,5,2] => 11000010 => [1,1,5,2]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,5,2] => 11000010 => [1,1,5,2]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,5,2] => 11000010 => [1,1,5,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1] => 11000011 => [1,1,5,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,5,2] => 11000010 => [1,1,5,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => 11000001 => [1,1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,6,1] => 11000001 => [1,1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,6,1] => 11000001 => [1,1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,6,1] => 11000001 => [1,1,6,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,6,1] => 11000001 => [1,1,6,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,6,1] => 11000001 => [1,1,6,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => 11000000 => [1,1,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => [1,2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => [1,2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 10111100 => [1,2,1,1,1,3]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 10111010 => [1,2,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 10111010 => [1,2,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 10111000 => [1,2,1,1,4]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 10110100 => [1,2,1,2,3]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 10110100 => [1,2,1,2,3]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 10110000 => [1,2,1,5]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => [1,2,2,1,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 10101000 => [1,2,2,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => [1,2,2,1,3]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 10101100 => [1,2,2,1,3]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => 10101000 => [1,2,2,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => 10100100 => [1,2,3,3]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,3] => 10100100 => [1,2,3,3]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,3] => 10100100 => [1,2,3,3]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => 10100010 => [1,2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,2] => 10100010 => [1,2,4,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,2] => 10100010 => [1,2,4,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,2] => 10100010 => [1,2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => 10100000 => [1,2,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => [1,2,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => [1,2,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 10111100 => [1,2,1,1,1,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 10111010 => [1,2,1,1,2,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 10111010 => [1,2,1,1,2,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 10111000 => [1,2,1,1,4]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 10110100 => [1,2,1,2,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 10110100 => [1,2,1,2,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 10110000 => [1,2,1,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => [1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 10111100 => [1,2,1,1,1,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 10111010 => [1,2,1,1,2,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 10111010 => [1,2,1,1,2,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 10111000 => [1,2,1,1,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => [1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,3] => 10111100 => [1,2,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => [1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => 10111110 => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => 10111111 => [1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1] => 10111111 => [1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,2] => 10111110 => [1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,2,1] => 10111101 => [1,2,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,3] => 10111100 => [1,2,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,2,2] => 10111010 => [1,2,1,1,2,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,2,2] => 10111010 => [1,2,1,1,2,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1] => 10111011 => [1,2,1,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,2,2] => 10111010 => [1,2,1,1,2,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,3,1] => 10111001 => [1,2,1,1,3,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,4] => 10111000 => [1,2,1,1,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,2,3] => 10110100 => [1,2,1,2,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,2,3] => 10110100 => [1,2,1,2,3]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1] => 10110111 => [1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,2] => 10110110 => [1,2,1,2,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,1] => 10110101 => [1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,2,3] => 10110100 => [1,2,1,2,3]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1] => 10110011 => [1,2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,1,3,2] => 10110010 => [1,2,1,3,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,4,1] => 10110001 => [1,2,1,4,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,5] => 10110000 => [1,2,1,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => [1,2,2,1,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 10101000 => [1,2,2,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => [1,2,2,1,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 10101100 => [1,2,2,1,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => 10101000 => [1,2,2,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,2,1,3] => 10101100 => [1,2,2,1,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,2,1,3] => 10101100 => [1,2,2,1,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1] => 10101111 => [1,2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,2] => 10101110 => [1,2,2,1,1,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,1] => 10101101 => [1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,3] => 10101100 => [1,2,2,1,3]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1] => 10101011 => [1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2] => 10101010 => [1,2,2,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,2,3,1] => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,4] => 10101000 => [1,2,2,4]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,3] => 10100100 => [1,2,3,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,3] => 10100100 => [1,2,3,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,3] => 10100100 => [1,2,3,3]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1] => 10100111 => [1,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,1,2] => 10100110 => [1,2,3,1,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,2,1] => 10100101 => [1,2,3,2,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,3] => 10100100 => [1,2,3,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,2] => 10100010 => [1,2,4,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,4,2] => 10100010 => [1,2,4,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,4,2] => 10100010 => [1,2,4,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,4,2] => 10100010 => [1,2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1] => 10100011 => [1,2,4,1,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,2] => 10100010 => [1,2,4,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,5,1] => 10100001 => [1,2,5,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,6] => 10100000 => [1,2,6]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => 10011000 => [1,3,1,4]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 10010100 => [1,3,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,3] => 10010100 => [1,3,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => 10010000 => [1,3,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 10011000 => [1,3,1,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 10011000 => [1,3,1,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,3] => 10010100 => [1,3,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,2,3] => 10010100 => [1,3,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,3] => 10010100 => [1,3,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,5] => 10010000 => [1,3,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 10011000 => [1,3,1,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 10011000 => [1,3,1,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1] => 10011111 => [1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,2] => 10011110 => [1,3,1,1,1,2]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,1] => 10011101 => [1,3,1,1,2,1]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,3] => 10011100 => [1,3,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1] => 10011011 => [1,3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,2,2] => 10011010 => [1,3,1,2,2]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,3,1] => 10011001 => [1,3,1,3,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,4] => 10011000 => [1,3,1,4]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,2,3] => 10010100 => [1,3,2,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,2,3] => 10010100 => [1,3,2,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,2,3] => 10010100 => [1,3,2,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 10010111 => [1,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,2] => 10010110 => [1,3,2,1,2]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 10010101 => [1,3,2,2,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,2,3] => 10010100 => [1,3,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1] => 10010011 => [1,3,3,1,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 10010010 => [1,3,3,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,1] => 10010001 => [1,3,4,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,5] => 10010000 => [1,3,5]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 10001000 => [1,4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4] => 10001000 => [1,4,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4] => 10001000 => [1,4,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1] => 10001111 => [1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,2] => 10001110 => [1,4,1,1,2]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,2,1] => 10001101 => [1,4,1,2,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,3] => 10001100 => [1,4,1,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1] => 10001011 => [1,4,2,1,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,2,2] => 10001010 => [1,4,2,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,1] => 10001001 => [1,4,3,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,4] => 10001000 => [1,4,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => 10000100 => [1,5,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,3] => 10000100 => [1,5,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,3] => 10000100 => [1,5,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,3] => 10000100 => [1,5,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1] => 10000111 => [1,5,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,2] => 10000110 => [1,5,1,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,2,1] => 10000101 => [1,5,2,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,3] => 10000100 => [1,5,3]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => 10000010 => [1,6,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,2] => 10000010 => [1,6,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,2] => 10000010 => [1,6,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,2] => 10000010 => [1,6,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,2] => 10000010 => [1,6,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1] => 10000011 => [1,6,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,2] => 10000010 => [1,6,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => 10000001 => [1,7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1] => 10000001 => [1,7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1] => 10000001 => [1,7,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1] => 10000001 => [1,7,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1] => 10000001 => [1,7,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1] => 10000001 => [1,7,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,1] => 10000001 => [1,7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => 10000000 => [1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => 100000001 => [1,8,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => 110000000 => [1,1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1000000001 => [1,9,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,7,1] => 110000001 => [1,1,7,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,9] => 1100000000 => [1,1,9]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,7,1] => 110000001 => [1,1,7,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,6,2] => 110000010 => [1,1,6,2]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,8,1] => 1100000001 => [1,1,8,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,10] => 11000000000 => [1,1,10]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1] => 100000000001 => [1,11,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,7,1] => 110000001 => [1,1,7,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,8,1] => 1100000001 => [1,1,8,1]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,5,3] => 110000100 => [1,1,5,3]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,7,2] => 1100000010 => [1,1,7,2]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,9,1] => 11000000001 => [1,1,9,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [6,3,1] => 1000001001 => [1,6,3,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,7,1] => 110000001 => [1,1,7,1]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,8,1] => 1100000001 => [1,1,8,1]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,6,2] => 110000010 => [1,1,6,2]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,5,2,1] => 110000101 => [1,1,5,2,1]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,7,1,1] => 1100000011 => [1,1,7,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,9,1] => 11000000001 => [1,1,9,1]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,4,4] => 110001000 => [1,1,4,4]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,8,2] => 11000000010 => [1,1,8,2]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [6,2,1,1] => 1000001011 => [1,6,2,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,7,1] => 110000001 => [1,1,7,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,8,1] => 1100000001 => [1,1,8,1]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,5,2,1] => 110000101 => [1,1,5,2,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,7,1,1] => 1100000011 => [1,1,7,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,9,1] => 11000000001 => [1,1,9,1]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,5,1,2] => 110000110 => [1,1,5,1,2]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,7,2] => 1100000010 => [1,1,7,2]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,4,3,1] => 110001001 => [1,1,4,3,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,8,1,1] => 11000000011 => [1,1,8,1,1]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,5] => 110010000 => [1,1,3,5]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,5,4] => 1100001000 => [1,1,5,4]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,1,2,1] => 1000001101 => [1,6,1,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [4,2,2,1] => 100010101 => [1,4,2,2,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => 100000010 => [1,7,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,7,1] => 110000001 => [1,1,7,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,8,1] => 1100000001 => [1,1,8,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,6,2] => 110000010 => [1,1,6,2]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1,1] => 110000111 => [1,1,5,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,7,1,1] => 1100000011 => [1,1,7,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,4,2,2] => 110001010 => [1,1,4,2,2]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,6,1,2] => 1100000110 => [1,1,6,1,2]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,1] => 110010001 => [1,1,3,4,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => 101000000 => [1,2,7]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,6] => 110100000 => [1,1,2,6]
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,6,4] => 11000001000 => [1,1,6,4]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [6,3,1] => 1000001001 => [1,6,3,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => 110000001 => [1,1,7,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,8,1] => 1100000001 => [1,1,8,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1,1] => 110000111 => [1,1,5,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,4,3,1] => 110001001 => [1,1,4,3,1]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,5,1,2] => 110000110 => [1,1,5,1,2]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,7,2] => 1100000010 => [1,1,7,2]
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,5,2,1] => 110000101 => [1,1,5,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,4,2,1,1] => 110001011 => [1,1,4,2,1,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,6,1,1,1] => 1100000111 => [1,1,6,1,1,1]
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,4,1,3] => 110001100 => [1,1,4,1,3]
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,5,2,2] => 1100001010 => [1,1,5,2,2]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,5,1] => 110100001 => [1,1,2,5,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => 111000000 => [1,1,1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,7,1] => 1010000001 => [1,2,7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => 1000000010 => [1,8,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [2,4,2,1] => 101000101 => [1,2,4,2,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,8,1] => 1100000001 => [1,1,8,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [5,2,2] => 100001010 => [1,5,2,2]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1,1] => 110000111 => [1,1,5,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,4,2,2] => 110001010 => [1,1,4,2,2]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,3,1,1] => 110010011 => [1,1,3,3,1,1]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,5,1] => 110100001 => [1,1,2,5,1]
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,5,1,3] => 1100001100 => [1,1,5,1,3]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,5,2] => 101000010 => [1,2,5,2]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,6,1] => 111000001 => [1,1,1,6,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,8] => 1010000000 => [1,2,8]
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,4,6] => 11000100000 => [1,1,4,6]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,8,1] => 1100000001 => [1,1,8,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2] => 1000000110 => [1,7,1,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,5,2,1] => 110000101 => [1,1,5,2,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,1,2] => 100001110 => [1,5,1,1,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,3,2] => 100010010 => [1,4,3,2]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,4,2,1,1] => 110001011 => [1,1,4,2,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,1] => 110010001 => [1,1,3,4,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,5,1,1,1] => 110000111 => [1,1,5,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,4,2,1,1] => 110001011 => [1,1,4,2,1,1]
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,5,3] => 110000100 => [1,1,5,3]
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,1,2] => 110001110 => [1,1,4,1,1,2]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,4,1,1] => 110100011 => [1,1,2,4,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,6,1] => 111000001 => [1,1,1,6,1]
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,1,4] => 110011000 => [1,1,3,1,4]
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,4,3] => 101000100 => [1,2,4,3]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,5,2] => 111000010 => [1,1,1,5,2]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,7,1] => 1010000001 => [1,2,7,1]
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,6,1] => 1101000001 => [1,1,2,6,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1,1] => 101111111 => [1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,1,2] => 101111110 => [1,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,1,3] => 101111100 => [1,2,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,1,2,2] => 101111010 => [1,2,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,1,2,2] => 101111010 => [1,2,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,1,3,1] => 101111001 => [1,2,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,1,3,1] => 101111001 => [1,2,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1,3,1] => 101111001 => [1,2,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,1,4] => 101111000 => [1,2,1,1,1,4]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,1,2,1,2] => 101110110 => [1,2,1,1,2,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => 101110100 => [1,2,1,1,2,3]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,1,2,1,2] => 101110110 => [1,2,1,1,2,1,2]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,1,2,3] => 101110100 => [1,2,1,1,2,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,1,3,1,1] => 101110011 => [1,2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,1,3,1,1] => 101110011 => [1,2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,1,3,1,1] => 101110011 => [1,2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,1,3,1,1] => 101110011 => [1,2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,1,3,1,1] => 101110011 => [1,2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,1,4,1] => 101110001 => [1,2,1,1,4,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,1,4,1] => 101110001 => [1,2,1,1,4,1]
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,4,1] => 101110001 => [1,2,1,1,4,1]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,1,5] => 101110000 => [1,2,1,1,5]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,2,1,1,2] => 101101110 => [1,2,1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1,2,1] => 101101101 => [1,2,1,2,1,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1,2,1] => 101101101 => [1,2,1,2,1,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,2,2,1,1] => 101101011 => [1,2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,2,2,1,1] => 101101011 => [1,2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,2,2,1,1] => 101101011 => [1,2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,2,4] => 101101000 => [1,2,1,2,4]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,1,2,1,3] => 101101100 => [1,2,1,2,1,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,1,2] => 101101110 => [1,2,1,2,1,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,1,2,2,1,1] => 101101011 => [1,2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,1,2,2,1,1] => 101101011 => [1,2,1,2,2,1,1]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,1,2,4] => 101101000 => [1,2,1,2,4]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,4,2] => 101100010 => [1,2,1,4,2]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,4,1,1] => 101100011 => [1,2,1,4,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,1,4,2] => 101100010 => [1,2,1,4,2]
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,4,1,1] => 101100011 => [1,2,1,4,1,1]
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1,4,1,1] => 101100011 => [1,2,1,4,1,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,5,1] => 101100001 => [1,2,1,5,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,5,1] => 101100001 => [1,2,1,5,1]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,5,1] => 101100001 => [1,2,1,5,1]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,5,1] => 101100001 => [1,2,1,5,1]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,6] => 101100000 => [1,2,1,6]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => 101011110 => [1,2,2,1,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,1,2,1] => 101011101 => [1,2,2,1,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1] => 101011011 => [1,2,2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,2,1,1] => 101011011 => [1,2,2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,2,1,1] => 101011011 => [1,2,2,1,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [2,2,1,3,1] => 101011001 => [1,2,2,1,3,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1] => 101010111 => [1,2,2,2,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,2,1,2] => 101010110 => [1,2,2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2,3] => 101010100 => [1,2,2,2,3]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,2,3,1,1] => 101010011 => [1,2,2,3,1,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [2,2,3,1,1] => 101010011 => [1,2,2,3,1,1]
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,3,2] => 101010010 => [1,2,2,3,2]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,5] => 101010000 => [1,2,2,5]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => 101011110 => [1,2,2,1,1,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,1,2,1] => 101011101 => [1,2,2,1,1,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1] => 101011011 => [1,2,2,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,1,2,1,1] => 101011011 => [1,2,2,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,1,4] => 101011000 => [1,2,2,1,4]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,1,2] => 101011110 => [1,2,2,1,1,1,2]
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,1,2,1] => 101011101 => [1,2,2,1,1,2,1]
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,1,3] => 101011100 => [1,2,2,1,1,3]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,1,3,1] => 101011001 => [1,2,2,1,3,1]
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,1,4] => 101011000 => [1,2,2,1,4]
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [2,2,2,1,2] => 101010110 => [1,2,2,2,1,2]
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1,1] => 101010111 => [1,2,2,2,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [2,2,3,1,1] => 101010011 => [1,2,2,3,1,1]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,5] => 101010000 => [1,2,2,5]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [2,3,1,2,1] => 101001101 => [1,2,3,1,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [2,3,2,1,1] => 101001011 => [1,2,3,2,1,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [2,3,3,1] => 101001001 => [1,2,3,3,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [2,3,1,2,1] => 101001101 => [1,2,3,1,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [2,3,1,3] => 101001100 => [1,2,3,1,3]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [2,4,3] => 101000100 => [1,2,4,3]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [2,4,3] => 101000100 => [1,2,4,3]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [2,4,1,2] => 101000110 => [1,2,4,1,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,4,2,1] => 101000101 => [1,2,4,2,1]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,4,3] => 101000100 => [1,2,4,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,5,2] => 101000010 => [1,2,5,2]
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [2,5,2] => 101000010 => [1,2,5,2]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [2,5,2] => 101000010 => [1,2,5,2]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,5,2] => 101000010 => [1,2,5,2]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,5,2] => 101000010 => [1,2,5,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,7] => 101000000 => [1,2,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => 100111100 => [1,3,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,3,2] => 100110010 => [1,3,1,3,2]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,1] => 100110001 => [1,3,1,4,1]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,5] => 100110000 => [1,3,1,5]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,2,1,1,2] => 100101110 => [1,3,2,1,1,2]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,2,1,3] => 100101100 => [1,3,2,1,3]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,2,4] => 100101000 => [1,3,2,4]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2] => 100100010 => [1,3,4,2]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,6] => 100100000 => [1,3,6]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,1,4] => 100111000 => [1,3,1,1,4]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,1] => 100110001 => [1,3,1,4,1]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,5] => 100110000 => [1,3,1,5]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => 100111100 => [1,3,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,1,4] => 100111000 => [1,3,1,1,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => 100111100 => [1,3,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,1,3] => 100111100 => [1,3,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,1,2,2] => 100111010 => [1,3,1,1,2,2]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,1,3,1] => 100111001 => [1,3,1,1,3,1]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,1,3,1] => 100111001 => [1,3,1,1,3,1]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,1,4] => 100111000 => [1,3,1,1,4]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,1,2,2,1] => 100110101 => [1,3,1,2,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,4,1] => 100110001 => [1,3,1,4,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,4,1] => 100110001 => [1,3,1,4,1]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,5] => 100110000 => [1,3,1,5]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [3,2,1,2,1] => 100101101 => [1,3,2,1,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,1,2] => 100101110 => [1,3,2,1,1,2]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,1,2] => 100101110 => [1,3,2,1,1,2]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [3,2,3,1] => 100101001 => [1,3,2,3,1]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,2,4] => 100101000 => [1,3,2,4]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [3,3,1,2] => 100100110 => [1,3,3,1,2]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [3,3,2,1] => 100100101 => [1,3,3,2,1]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 100100100 => [1,3,3,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [3,3,1,2] => 100100110 => [1,3,3,1,2]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,1,2] => 100100110 => [1,3,3,1,2]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [3,3,2,1] => 100100101 => [1,3,3,2,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [3,3,2,1] => 100100101 => [1,3,3,2,1]
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 100100100 => [1,3,3,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [3,4,2] => 100100010 => [1,3,4,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [3,4,2] => 100100010 => [1,3,4,2]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,4,2] => 100100010 => [1,3,4,2]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2] => 100100010 => [1,3,4,2]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,6] => 100100000 => [1,3,6]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,1,1,3] => 100011100 => [1,4,1,1,3]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,1,3,1] => 100011001 => [1,4,1,3,1]
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => 100011000 => [1,4,1,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2,1] => 100010101 => [1,4,2,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,2,3] => 100010100 => [1,4,2,3]
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [4,2,3] => 100010100 => [1,4,2,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2] => 100010010 => [1,4,3,2]
[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0] => [4,3,2] => 100010010 => [1,4,3,2]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5] => 100010000 => [1,4,5]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,2,2] => 100011010 => [1,4,1,2,2]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => 100011000 => [1,4,1,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,1,1,3] => 100011100 => [1,4,1,1,3]
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,2,2] => 100011010 => [1,4,1,2,2]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,1,2,2] => 100011010 => [1,4,1,2,2]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,3,1] => 100011001 => [1,4,1,3,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5] => 100010000 => [1,4,5]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,1,3,1] => 100011001 => [1,4,1,3,1]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => 100011000 => [1,4,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,4] => 100011000 => [1,4,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,1,3] => 100011100 => [1,4,1,1,3]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,1,3] => 100011100 => [1,4,1,1,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,1,3] => 100011100 => [1,4,1,1,3]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,2] => 100011010 => [1,4,1,2,2]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,1,3,1] => 100011001 => [1,4,1,3,1]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,1,3,1] => 100011001 => [1,4,1,3,1]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,1,4] => 100011000 => [1,4,1,4]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,2,1,2] => 100010110 => [1,4,2,1,2]
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [4,2,1,2] => 100010110 => [1,4,2,1,2]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,2,2,1] => 100010101 => [1,4,2,2,1]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [4,2,3] => 100010100 => [1,4,2,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0] => [4,3,2] => 100010010 => [1,4,3,2]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,3,2] => 100010010 => [1,4,3,2]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,3,2] => 100010010 => [1,4,3,2]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [4,3,2] => 100010010 => [1,4,3,2]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,5] => 100010000 => [1,4,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4] => 100001000 => [1,5,4]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,1,1,2] => 100001110 => [1,5,1,1,2]
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,2,2] => 100001010 => [1,5,2,2]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,4] => 100001000 => [1,5,4]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [5,1,1,2] => 100001110 => [1,5,1,1,2]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,2,2] => 100001010 => [1,5,2,2]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [5,2,2] => 100001010 => [1,5,2,2]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,1,2] => 100001110 => [1,5,1,1,2]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,1,2] => 100001110 => [1,5,1,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,1,2] => 100001110 => [1,5,1,1,2]
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [5,2,2] => 100001010 => [1,5,2,2]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [5,2,2] => 100001010 => [1,5,2,2]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,4] => 100001000 => [1,5,4]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,3] => 100000100 => [1,6,3]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [6,3] => 100000100 => [1,6,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [6,3] => 100000100 => [1,6,3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [6,3] => 100000100 => [1,6,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,3] => 100000100 => [1,6,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,2] => 100000010 => [1,7,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [7,2] => 100000010 => [1,7,2]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [7,2] => 100000010 => [1,7,2]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [7,2] => 100000010 => [1,7,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,2] => 100000010 => [1,7,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,1,1] => 100000011 => [1,7,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,2] => 100000010 => [1,7,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 100000001 => [1,8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,1] => 100000001 => [1,8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,1] => 100000001 => [1,8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,1] => 100000001 => [1,8,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,1] => 100000001 => [1,8,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1] => 100000001 => [1,8,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,1] => 100000001 => [1,8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => 100000000 => [1,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1] => 111111111 => [1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => 111111110 => [1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,2,1] => 111111101 => [1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,2,1,1] => 111111011 => [1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1,1] => 111110111 => [1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1,1] => 111101111 => [1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1,1] => 111011111 => [1,1,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1,1] => 110111111 => [1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1] => 1111111111 => [1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2] => 1111111110 => [1,1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => 111111100 => [1,1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,2,1] => 1111111101 => [1,1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,3,1] => 111111001 => [1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,2,1,1] => 1111111011 => [1,1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,3,1,1] => 111110011 => [1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,3,1,1,1] => 111100111 => [1,1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => 111001111 => [1,1,1,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1,1,1] => 1110111111 => [1,1,1,2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1,1,1] => 1101111111 => [1,1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1,1,1] => 1011111111 => [1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,1] => 11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,2] => 11111111110 => [1,1,1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,3] => 1111111100 => [1,1,1,1,1,1,1,1,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,2,1] => 11111111101 => [1,1,1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,3,1] => 111111001 => [1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,3,1] => 1111111001 => [1,1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,3,1,1] => 111110011 => [1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => 111111000 => [1,1,1,1,1,1,4]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1,1] => 111100111 => [1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,4,1] => 111110001 => [1,1,1,1,1,4,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => 111001111 => [1,1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,4,1,1] => 111100011 => [1,1,1,1,4,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1,1] => 1100111111 => [1,1,3,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1,1,1,1] => 10111111111 => [1,2,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,3,1] => 1111111001 => [1,1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,3,1,1] => 111110011 => [1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,3,1,1] => 1111110011 => [1,1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1,1] => 111100111 => [1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,3,2] => 111110010 => [1,1,1,1,1,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,3,1,1,1] => 1111100111 => [1,1,1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => 111001111 => [1,1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,3,1,1,1,1] => 1111001111 => [1,1,1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,4,1] => 111110001 => [1,1,1,1,1,4,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,3,2,1,1] => 111001011 => [1,1,1,3,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1,1,1] => 1110011111 => [1,1,1,3,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,4,1,1] => 111100011 => [1,1,1,1,4,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1,1] => 1100111111 => [1,1,3,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1,1] => 111000111 => [1,1,1,4,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,1,3,1] => 11111111001 => [1,1,1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,3,1,1] => 1111110011 => [1,1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1,1] => 111100111 => [1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,3,2] => 1111110010 => [1,1,1,1,1,1,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,3,1,2] => 111100110 => [1,1,1,1,3,1,2]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,5] => 111110000 => [1,1,1,1,1,5]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,4,1] => 1111110001 => [1,1,1,1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,3,2,1] => 111100101 => [1,1,1,1,3,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,1,2,1,1] => 110011011 => [1,1,3,1,2,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,5,1,1] => 111000011 => [1,1,1,5,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,3,2,1,1] => 111001011 => [1,1,1,3,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,4,1,1,1] => 111000111 => [1,1,1,4,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1,1] => 1001011111 => [1,3,2,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,3,1,1,1] => 1111100111 => [1,1,1,1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1,1] => 111001111 => [1,1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,5] => 1111110000 => [1,1,1,1,1,1,5]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,1,2] => 111001110 => [1,1,1,3,1,1,2]
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,5,1] => 111100001 => [1,1,1,1,5,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,3,1,1] => 110010011 => [1,1,3,3,1,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,1,2,1,1] => 110011011 => [1,1,3,1,2,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,5,1,1] => 111000011 => [1,1,1,5,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1,1,1] => 1111001111 => [1,1,1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,3,1,1,2] => 1111001110 => [1,1,1,1,3,1,1,2]
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,1,2] => 110011110 => [1,1,3,1,1,1,2]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,5,1] => 111100001 => [1,1,1,1,5,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,5,1,1] => 111000011 => [1,1,1,5,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6] => 111100000 => [1,1,1,1,6]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,3,1,1] => 110010011 => [1,1,3,3,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1,1] => 110010111 => [1,1,3,2,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1,1,1] => 1110011111 => [1,1,1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,1,1,2] => 1110011110 => [1,1,1,3,1,1,1,2]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,5,1] => 1111100001 => [1,1,1,1,1,5,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,3,3,1] => 111001001 => [1,1,1,3,3,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,6] => 1111100000 => [1,1,1,1,1,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,1,1,2,1,1] => 1001111011 => [1,3,1,1,1,2,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,3,3,1,1] => 1110010011 => [1,1,1,3,3,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,6,1] => 111000001 => [1,1,1,6,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1,1,1] => 1100111111 => [1,1,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,5,1] => 11111100001 => [1,1,1,1,1,1,5,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,5,1,1] => 111000011 => [1,1,1,5,1,1]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,1,3,1,1] => 1001110011 => [1,3,1,1,3,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,1,1,1,1,1] => 10000011111 => [1,6,1,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1,1,1] => 1001011111 => [1,3,2,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,2,1] => 111111101 => [1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,2,1,1] => 111111011 => [1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,2,2] => 111111010 => [1,1,1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,3,1] => 111111001 => [1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1] => 111110111 => [1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,2,1,2] => 111110110 => [1,1,1,1,1,2,1,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,2,2,1] => 111110101 => [1,1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,2,3] => 111110100 => [1,1,1,1,1,2,3]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => 111110011 => [1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,3,2] => 111110010 => [1,1,1,1,1,3,2]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,4,1] => 111110001 => [1,1,1,1,1,4,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => 111101111 => [1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1,2,1] => 111101101 => [1,1,1,1,2,1,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,2,2,1,1] => 111101011 => [1,1,1,1,2,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2,2] => 111101010 => [1,1,1,1,2,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,2,4] => 111101000 => [1,1,1,1,2,4]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => 111100111 => [1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,3,2,1] => 111100101 => [1,1,1,1,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,3,3] => 111100100 => [1,1,1,1,3,3]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,5,1] => 111100001 => [1,1,1,1,5,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => 111011111 => [1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => 111011110 => [1,1,1,2,1,1,1,2]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,2,1,1,2,1] => 111011101 => [1,1,1,2,1,1,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,2,1,1,3] => 111011100 => [1,1,1,2,1,1,3]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1] => 111010111 => [1,1,1,2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,2,1] => 111010101 => [1,1,1,2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,2,4,1] => 111010001 => [1,1,1,2,4,1]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,2,5] => 111010000 => [1,1,1,2,5]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => 111001111 => [1,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => 111000111 => [1,1,1,4,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => 111000100 => [1,1,1,4,3]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,5,1,1] => 111000011 => [1,1,1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,5,2] => 111000010 => [1,1,1,5,2]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => 111000001 => [1,1,1,6,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 110111111 => [1,1,2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => 110111110 => [1,1,2,1,1,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,2,1] => 110111101 => [1,1,2,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 110111100 => [1,1,2,1,1,1,3]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,1,2,1,1] => 110111011 => [1,1,2,1,1,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1] => 110110111 => [1,1,2,1,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,1,5] => 110110000 => [1,1,2,1,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => 110101111 => [1,1,2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,2,1,1] => 110101011 => [1,1,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,3,1,1,1] => 110100111 => [1,1,2,3,1,1,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,5,1] => 110100001 => [1,1,2,5,1]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => 110100000 => [1,1,2,6]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => 110010101 => [1,1,3,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => 110001100 => [1,1,4,1,3]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,1,1] => 110001011 => [1,1,4,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => 110001000 => [1,1,4,4]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => 110000111 => [1,1,5,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,5,3] => 110000100 => [1,1,5,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => 110000011 => [1,1,6,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => 110000010 => [1,1,6,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 101111111 => [1,2,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 101111110 => [1,2,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => 101111100 => [1,2,1,1,1,1,3]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => 101111010 => [1,2,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => 101111001 => [1,2,1,1,1,3,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 101111000 => [1,2,1,1,1,4]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => 101110100 => [1,2,1,1,2,3]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => 101110001 => [1,2,1,1,4,1]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => 101110000 => [1,2,1,1,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => 101100001 => [1,2,1,5,1]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => 101100000 => [1,2,1,6]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,2,1,1,1,2] => 101011110 => [1,2,2,1,1,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,2,1,2] => 101010110 => [1,2,2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,2,3] => 101010100 => [1,2,2,2,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,2,3,1,1] => 101010011 => [1,2,2,3,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,2,3,2] => 101010010 => [1,2,2,3,2]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,5] => 101010000 => [1,2,2,5]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => 101001001 => [1,2,3,3,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => 101000100 => [1,2,4,3]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,5,2] => 101000010 => [1,2,5,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,1,3] => 100111100 => [1,3,1,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,1,2] => 100110110 => [1,3,1,2,1,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 100110101 => [1,3,1,2,2,1]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 100110001 => [1,3,1,4,1]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 100110000 => [1,3,1,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 100100100 => [1,3,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,2] => 100100010 => [1,3,4,2]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => 100100000 => [1,3,6]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,1,1,3] => 100011100 => [1,4,1,1,3]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 100011001 => [1,4,1,3,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,4] => 100011000 => [1,4,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 100010101 => [1,4,2,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,2,3] => 100010100 => [1,4,2,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => 100010010 => [1,4,3,2]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 100010000 => [1,4,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => 100001110 => [1,5,1,1,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 100001000 => [1,5,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 100000100 => [1,6,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,2,1] => 1111111101 => [1,1,1,1,1,1,1,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,2,1,1] => 1111111011 => [1,1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,2,2] => 1111111010 => [1,1,1,1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,3,1] => 1111111001 => [1,1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,2,2,1] => 1111110101 => [1,1,1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,4,1] => 1111110001 => [1,1,1,1,1,1,4,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,3,1,1,1] => 1111100111 => [1,1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,5,1] => 1111100001 => [1,1,1,1,1,5,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,2,1,1,1,2] => 1111011110 => [1,1,1,1,2,1,1,1,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,2,1,1,1] => 1111010111 => [1,1,1,1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,2,1] => 1111010101 => [1,1,1,1,2,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1,1] => 1111001111 => [1,1,1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,4,2,1] => 1111000101 => [1,1,1,1,4,2,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,6,1] => 1111000001 => [1,1,1,1,6,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,7] => 1111000000 => [1,1,1,1,7]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1,1] => 1110111111 => [1,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1,1] => 1110101111 => [1,1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2,2] => 1110101010 => [1,1,1,2,2,2,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1,1] => 1110011111 => [1,1,1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,5,1,1,1] => 1110000111 => [1,1,1,5,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,6,2] => 1110000010 => [1,1,1,6,2]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,7,1] => 1110000001 => [1,1,1,7,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => 1101111111 => [1,1,2,1,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,1,2] => 1101111110 => [1,1,2,1,1,1,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,1,2,1] => 1101111101 => [1,1,2,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,1,3,1,2] => 1101100110 => [1,1,2,1,3,1,2]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1,1] => 1101011111 => [1,1,2,2,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,2,3] => 1101010100 => [1,1,2,2,2,3]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,4,1,1,1] => 1101000111 => [1,1,2,4,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1,1] => 1100111111 => [1,1,3,1,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2,2] => 1100101010 => [1,1,3,2,2,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => 1100001111 => [1,1,5,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4] => 1100001000 => [1,1,5,4]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,6,1,1,1] => 1100000111 => [1,1,6,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => 1100000011 => [1,1,7,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,7,2] => 1100000010 => [1,1,7,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => 1011111111 => [1,2,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => 1011111110 => [1,2,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,1,3] => 1011111100 => [1,2,1,1,1,1,1,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,1,4] => 1011111000 => [1,2,1,1,1,1,4]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,1,5] => 1011110000 => [1,2,1,1,1,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1,1] => 1011011111 => [1,2,1,2,1,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,6,1] => 1011000001 => [1,2,1,6,1]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,7] => 1011000000 => [1,2,1,7]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,2,1,2,1] => 1010101101 => [1,2,2,2,1,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,2,3,1] => 1010101001 => [1,2,2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,2,3,1,1,1] => 1010100111 => [1,2,2,3,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3,3] => 1010100100 => [1,2,2,3,3]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,6,2] => 1010000010 => [1,2,6,2]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,7,1] => 1010000001 => [1,2,7,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,1,2] => 1001111110 => [1,3,1,1,1,1,1,2]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,5,1] => 1001100001 => [1,3,1,5,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1,1] => 1001011111 => [1,3,2,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => 1001010101 => [1,3,2,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,2,3] => 1001010100 => [1,3,2,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,3,2,2] => 1001001010 => [1,3,3,2,2]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,7] => 1001000000 => [1,3,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,1,2] => 1000111110 => [1,4,1,1,1,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,1,4] => 1000111000 => [1,4,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,4,1] => 1000110001 => [1,4,1,4,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => 1000101010 => [1,4,2,2,2]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,6] => 1000100000 => [1,4,6]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [5,1,1,1,2] => 1000011110 => [1,5,1,1,1,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [5,1,3,1] => 1000011001 => [1,5,1,3,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => 1000010101 => [1,5,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5] => 1000010000 => [1,5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [6,1,1,2] => 1000001110 => [1,6,1,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => 1000001101 => [1,6,1,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => 1000001001 => [1,6,3,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [7,1,2] => 1000000110 => [1,7,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,3] => 1000000100 => [1,7,3]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10] => 1000000000 => [1,10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 101111111 => [1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 101111111 => [1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 101111111 => [1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 101111111 => [1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 101111111 => [1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1] => 101111111 => [1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => 1011111111 => [1,2,1,1,1,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => 1011111111 => [1,2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => 1011111111 => [1,2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => 1011111111 => [1,2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => 1011111111 => [1,2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => 1011111111 => [1,2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1,1] => 1011111111 => [1,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,1,1,2] => 1000011110 => [1,5,1,1,1,2]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,1,1,1,2] => 10000111110 => [1,5,1,1,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,1,1,2] => 1000111110 => [1,4,1,1,1,1,2]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,1,1,1,1,1] => 10000011111 => [1,6,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => 10111111111 => [1,2,1,1,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,1,1,2] => 1011111110 => [1,2,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,2] => 1000000010 => [1,8,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,1] => 1000000001 => [1,9,1]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [9,2] => 10000000010 => [1,9,2]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [7,1,2] => 1000000110 => [1,7,1,2]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,2,1] => 110111101 => [1,1,2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 101111110 => [1,2,1,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,8] => 1010000000 => [1,2,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => 1000000001 => [1,9,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,1] => 1000000001 => [1,9,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [7,3] => 1000000100 => [1,7,3]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,5] => 1000010000 => [1,5,5]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,6] => 1000100000 => [1,4,6]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,7] => 1001000000 => [1,3,7]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => 101100000 => [1,2,1,6]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 100110000 => [1,3,1,5]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,4] => 100011000 => [1,4,1,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 110111111 => [1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => 111011111 => [1,1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 101111110 => [1,2,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1,1] => 1011011111 => [1,2,1,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1,1,1] => 1100001111 => [1,1,5,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,1,2] => 110111110 => [1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,1,2] => 101111110 => [1,2,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => 101111100 => [1,2,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,1,1,3] => 1011111100 => [1,2,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 101111000 => [1,2,1,1,1,4]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => 101110001 => [1,2,1,1,4,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,4,1,1] => 101100011 => [1,2,1,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,5] => 101010000 => [1,2,2,5]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,4,2] => 100100010 => [1,3,4,2]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3] => 100100100 => [1,3,3,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [4,2,3] => 100010100 => [1,4,2,3]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,1] => 1000000001 => [1,9,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,1] => 1000000001 => [1,9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,1] => 1000000001 => [1,9,1]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,1] => 1000000001 => [1,9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,1] => 1000000001 => [1,9,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,2,1,1] => 111011011 => [1,1,1,2,1,2,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [6,1,2] => 100000110 => [1,6,1,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,6,1] => 101000001 => [1,2,6,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1,1] => 111110111 => [1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1,1] => 111110111 => [1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1,1] => 1110111111 => [1,1,1,2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => 1101111111 => [1,1,2,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,1,1,2,1,1,1] => 1011110111 => [1,2,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,2,1,2] => 111110110 => [1,1,1,1,1,2,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,1,1,2,1,1,1] => 1011110111 => [1,2,1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,1,1,2,1,1,1] => 1011110111 => [1,2,1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1,1] => 1011110111 => [1,2,1,1,1,2,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,2,1,2] => 101010110 => [1,2,2,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,2,1,2,2] => 101011010 => [1,2,2,1,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => 101101010 => [1,2,1,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [2,3,1,2,1] => 101001101 => [1,2,3,1,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [2,2,3,1,1] => 101010011 => [1,2,2,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,2,1,1,1] => 101010111 => [1,2,2,2,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,2,1,3,1] => 101011001 => [1,2,2,1,3,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,2,1,2,1] => 1010101101 => [1,2,2,2,1,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,3,1,2] => 101100110 => [1,2,1,3,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,1,2,2,1] => 1010110101 => [1,2,2,1,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,1,2,2] => 110011010 => [1,1,3,1,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,2,1] => 1011010101 => [1,2,1,2,2,2,1]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,7] => 1011000000 => [1,2,1,7]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,1,6] => 1011100000 => [1,2,1,1,6]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,1,1,5] => 1011110000 => [1,2,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,1,1,4] => 1011111000 => [1,2,1,1,1,1,4]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1,1,1] => 1011011111 => [1,2,1,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,1,1,1,2,1] => 10111111101 => [1,2,1,1,1,1,1,1,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,2] => 1000000010 => [1,8,2]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [8,2] => 1000000010 => [1,8,2]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [7,3] => 1000000100 => [1,7,3]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [7,3] => 1000000100 => [1,7,3]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,2,3,1,1] => 1101010011 => [1,1,2,2,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,2,3,1,2,1] => 1101001101 => [1,1,2,3,1,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,2,3,2,1,1] => 1101001011 => [1,1,2,3,2,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,2,4,1,1,1] => 1101000111 => [1,1,2,4,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,2,1] => 1100110101 => [1,1,3,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,1,3,1,1] => 1100110011 => [1,1,3,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,3,2,1,2,1] => 1100101101 => [1,1,3,2,1,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,4,1,1,2,1] => 1100011101 => [1,1,4,1,1,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,2,1,1] => 1100101011 => [1,1,3,2,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,3,3,1,1,1] => 1100100111 => [1,1,3,3,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,4,1,2,1,1] => 1100011011 => [1,1,4,1,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,4,2,1,1,1] => 1100010111 => [1,1,4,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,5,1,1,1,1] => 1100001111 => [1,1,5,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,2,1] => 1011010101 => [1,2,1,2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,2,3,1,1] => 1011010011 => [1,2,1,2,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,1,3,1,2,1] => 1011001101 => [1,2,1,3,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,1,3,2,1,1] => 1011001011 => [1,2,1,3,2,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,1,4,1,1,1] => 1011000111 => [1,2,1,4,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,1,2,2,1] => 1010110101 => [1,2,2,1,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,2,1,3,1,1] => 1010110011 => [1,2,2,1,3,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,1,2,2,1] => 1001110101 => [1,3,1,1,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,1,3,1,1] => 1001110011 => [1,3,1,1,3,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [2,2,2,1,2,1] => 1010101101 => [1,2,2,2,1,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [2,3,1,1,2,1] => 1010011101 => [1,2,3,1,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1,2,1] => 1001101101 => [1,3,1,2,1,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [3,2,1,1,2,1] => 1001011101 => [1,3,2,1,1,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,1,1,2,1] => 1000111101 => [1,4,1,1,1,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [2,2,3,1,1,1] => 1010100111 => [1,2,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [2,3,1,2,1,1] => 1010011011 => [1,2,3,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [2,3,2,1,1,1] => 1010010111 => [1,2,3,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [2,4,1,1,1,1] => 1010001111 => [1,2,4,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,2,1,1] => 1001101011 => [1,3,1,2,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,1,3,1,1,1] => 1001100111 => [1,3,1,3,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,2,1,1] => 1001011011 => [1,3,2,1,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,1,2,1,1] => 1000111011 => [1,4,1,1,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [3,2,2,1,1,1] => 1001010111 => [1,3,2,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [3,3,1,1,1,1] => 1001001111 => [1,3,3,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,2,1,1,1] => 1000110111 => [1,4,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [4,2,1,1,1,1] => 1000101111 => [1,4,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,2,2,2,2,2,1] => 110101010101 => [1,1,2,2,2,2,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,2,2,2,3,1,1] => 110101010011 => [1,1,2,2,2,3,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [1,2,2,3,1,2,1] => 110101001101 => [1,1,2,2,3,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,2,3,2,1,1] => 110101001011 => [1,1,2,2,3,2,1,1]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [1,2,2,4,1,1,1] => 110101000111 => [1,1,2,2,4,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,1,2,2,1] => 110100110101 => [1,1,2,3,1,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,1,3,1,1] => 110100110011 => [1,1,2,3,1,3,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,3,2,1,2,1] => 110100101101 => [1,1,2,3,2,1,2,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [1,2,4,1,1,2,1] => 110100011101 => [1,1,2,4,1,1,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => [1,2,3,2,2,1,1] => 110100101011 => [1,1,2,3,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [1,2,3,3,1,1,1] => 110100100111 => [1,1,2,3,3,1,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,1,2,1,1] => 110100011011 => [1,1,2,4,1,2,1,1]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => [1,2,4,2,1,1,1] => 110100010111 => [1,1,2,4,2,1,1,1]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,2,5,1,1,1,1] => 110100001111 => [1,1,2,5,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,1,2,2,2,1] => 110011010101 => [1,1,3,1,2,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,3,1,2,3,1,1] => 110011010011 => [1,1,3,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,3,1,3,1,2,1] => 110011001101 => [1,1,3,1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,3,1,3,2,1,1] => 110011001011 => [1,1,3,1,3,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,3,1,4,1,1,1] => 110011000111 => [1,1,3,1,4,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1,2,2,1] => 110010110101 => [1,1,3,2,1,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,3,1,1] => 110010110011 => [1,1,3,2,1,3,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,1,1,2,2,1] => 110001110101 => [1,1,4,1,1,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1,3,1,1] => 110001110011 => [1,1,4,1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [1,3,2,2,1,2,1] => 110010101101 => [1,1,3,2,2,1,2,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [1,3,3,1,1,2,1] => 110010011101 => [1,1,3,3,1,1,2,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,4,1,2,1,2,1] => 110001101101 => [1,1,4,1,2,1,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [1,4,2,1,1,2,1] => 110001011101 => [1,1,4,2,1,1,2,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,1,1,1,2,1] => 110000111101 => [1,1,5,1,1,1,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [1,3,2,2,2,1,1] => 110010101011 => [1,1,3,2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [1,3,2,3,1,1,1] => 110010100111 => [1,1,3,2,3,1,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [1,3,3,1,2,1,1] => 110010011011 => [1,1,3,3,1,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [1,3,3,2,1,1,1] => 110010010111 => [1,1,3,3,2,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [1,3,4,1,1,1,1] => 110010001111 => [1,1,3,4,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,4,1,2,2,1,1] => 110001101011 => [1,1,4,1,2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,4,1,3,1,1,1] => 110001100111 => [1,1,4,1,3,1,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,1,2,1,1] => 110001011011 => [1,1,4,2,1,2,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,1,1,2,1,1] => 110000111011 => [1,1,5,1,1,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [1,4,2,2,1,1,1] => 110001010111 => [1,1,4,2,2,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [1,4,3,1,1,1,1] => 110001001111 => [1,1,4,3,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,5,1,2,1,1,1] => 110000110111 => [1,1,5,1,2,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,5,2,1,1,1,1] => 110000101111 => [1,1,5,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,1,1,1,1,1] => 110000011111 => [1,1,6,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,2,2,2,2,1] => 101101010101 => [1,2,1,2,2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [2,1,2,2,3,1,1] => 101101010011 => [1,2,1,2,2,3,1,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [2,1,2,3,1,2,1] => 101101001101 => [1,2,1,2,3,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [2,1,2,3,2,1,1] => 101101001011 => [1,2,1,2,3,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [2,1,2,4,1,1,1] => 101101000111 => [1,2,1,2,4,1,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,3,1,2,2,1] => 101100110101 => [1,2,1,3,1,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,3,1,1] => 101100110011 => [1,2,1,3,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [2,1,3,2,1,2,1] => 101100101101 => [1,2,1,3,2,1,2,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [2,1,4,1,1,2,1] => 101100011101 => [1,2,1,4,1,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [2,1,3,2,2,1,1] => 101100101011 => [1,2,1,3,2,2,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [2,1,3,3,1,1,1] => 101100100111 => [1,2,1,3,3,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [2,1,4,1,2,1,1] => 101100011011 => [1,2,1,4,1,2,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [2,1,4,2,1,1,1] => 101100010111 => [1,2,1,4,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,5,1,1,1,1] => 101100001111 => [1,2,1,5,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,2,2,1] => 101011010101 => [1,2,2,1,2,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,2,1,2,3,1,1] => 101011010011 => [1,2,2,1,2,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,3,1,2,1] => 101011001101 => [1,2,2,1,3,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,2,1,3,2,1,1] => 101011001011 => [1,2,2,1,3,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,2,1,4,1,1,1] => 101011000111 => [1,2,2,1,4,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,2,2,1] => 100111010101 => [1,3,1,1,2,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,1,1,2,3,1,1] => 100111010011 => [1,3,1,1,2,3,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,3,1,2,1] => 100111001101 => [1,3,1,1,3,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,1,3,2,1,1] => 100111001011 => [1,3,1,1,3,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,1,1,4,1,1,1] => 100111000111 => [1,3,1,1,4,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1,2,2,1] => 101010110101 => [1,2,2,2,1,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,2,2,1,3,1,1] => 101010110011 => [1,2,2,2,1,3,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,1,2,2,1] => 101001110101 => [1,2,3,1,1,2,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1,3,1,1] => 101001110011 => [1,2,3,1,1,3,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,2,1,2,2,1] => 100110110101 => [1,3,1,2,1,2,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,2,1,3,1,1] => 100110110011 => [1,3,1,2,1,3,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,1,2,2,1] => 100101110101 => [1,3,2,1,1,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,1,3,1,1] => 100101110011 => [1,3,2,1,1,3,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,1,1,1,2,2,1] => 100011110101 => [1,4,1,1,1,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [4,1,1,1,3,1,1] => 100011110011 => [1,4,1,1,1,3,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [2,2,2,2,1,2,1] => 101010101101 => [1,2,2,2,2,1,2,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [2,2,3,1,1,2,1] => 101010011101 => [1,2,2,3,1,1,2,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [2,3,1,2,1,2,1] => 101001101101 => [1,2,3,1,2,1,2,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [2,3,2,1,1,2,1] => 101001011101 => [1,2,3,2,1,1,2,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [2,4,1,1,1,2,1] => 101000111101 => [1,2,4,1,1,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [3,1,2,2,1,2,1] => 100110101101 => [1,3,1,2,2,1,2,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [3,1,3,1,1,2,1] => 100110011101 => [1,3,1,3,1,1,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,2,1,2,1,2,1] => 100101101101 => [1,3,2,1,2,1,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,1,2,1,2,1] => 100011101101 => [1,4,1,1,2,1,2,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [3,2,2,1,1,2,1] => 100101011101 => [1,3,2,2,1,1,2,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [3,3,1,1,1,2,1] => 100100111101 => [1,3,3,1,1,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1,1,2,1] => 100011011101 => [1,4,1,2,1,1,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,1,1,1,2,1] => 100010111101 => [1,4,2,1,1,1,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,1,1,1,1,2,1] => 100001111101 => [1,5,1,1,1,1,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [2,2,2,2,2,1,1] => 101010101011 => [1,2,2,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [2,2,2,3,1,1,1] => 101010100111 => [1,2,2,2,3,1,1,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [2,2,3,1,2,1,1] => 101010011011 => [1,2,2,3,1,2,1,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [2,2,3,2,1,1,1] => 101010010111 => [1,2,2,3,2,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => [2,2,4,1,1,1,1] => 101010001111 => [1,2,2,4,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [2,3,1,2,2,1,1] => 101001101011 => [1,2,3,1,2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [2,3,1,3,1,1,1] => 101001100111 => [1,2,3,1,3,1,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => [2,3,2,1,2,1,1] => 101001011011 => [1,2,3,2,1,2,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [2,4,1,1,2,1,1] => 101000111011 => [1,2,4,1,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => [2,3,2,2,1,1,1] => 101001010111 => [1,2,3,2,2,1,1,1]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => [2,3,3,1,1,1,1] => 101001001111 => [1,2,3,3,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [2,4,1,2,1,1,1] => 101000110111 => [1,2,4,1,2,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => [2,4,2,1,1,1,1] => 101000101111 => [1,2,4,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [2,5,1,1,1,1,1] => 101000011111 => [1,2,5,1,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [3,1,2,2,2,1,1] => 100110101011 => [1,3,1,2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [3,1,2,3,1,1,1] => 100110100111 => [1,3,1,2,3,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [3,1,3,1,2,1,1] => 100110011011 => [1,3,1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [3,1,3,2,1,1,1] => 100110010111 => [1,3,1,3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [3,1,4,1,1,1,1] => 100110001111 => [1,3,1,4,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,2,2,1,1] => 100101101011 => [1,3,2,1,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,3,1,1,1] => 100101100111 => [1,3,2,1,3,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,1,2,2,1,1] => 100011101011 => [1,4,1,1,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,3,1,1,1] => 100011100111 => [1,4,1,1,3,1,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => [3,2,2,1,2,1,1] => 100101011011 => [1,3,2,2,1,2,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [3,3,1,1,2,1,1] => 100100111011 => [1,3,3,1,1,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,1,2,1,1] => 100011011011 => [1,4,1,2,1,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1,2,1,1] => 100010111011 => [1,4,2,1,1,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [5,1,1,1,2,1,1] => 100001111011 => [1,5,1,1,1,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [3,2,2,2,1,1,1] => 100101010111 => [1,3,2,2,2,1,1,1]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => [3,2,3,1,1,1,1] => 100101001111 => [1,3,2,3,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [3,3,1,2,1,1,1] => 100100110111 => [1,3,3,1,2,1,1,1]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => [3,3,2,1,1,1,1] => 100100101111 => [1,3,3,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [3,4,1,1,1,1,1] => 100100011111 => [1,3,4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [4,1,2,2,1,1,1] => 100011010111 => [1,4,1,2,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [4,1,3,1,1,1,1] => 100011001111 => [1,4,1,3,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,2,1,2,1,1,1] => 100010110111 => [1,4,2,1,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,1,2,1,1,1] => 100001110111 => [1,5,1,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => [4,2,2,1,1,1,1] => 100010101111 => [1,4,2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [4,3,1,1,1,1,1] => 100010011111 => [1,4,3,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,2,1,1,1,1] => 100001101111 => [1,5,1,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,2,1,1,1,1,1] => 100001011111 => [1,5,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,1,1,1,1,1] => 100000111111 => [1,6,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11] => 10000000000 => [1,11]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,9] => 10100000000 => [1,2,9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,7,1] => 1010000001 => [1,2,7,1]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,9] => 10100000000 => [1,2,9]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [11,1] => 100000000001 => [1,11,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,7,1] => 1010000001 => [1,2,7,1]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,6,2] => 1010000010 => [1,2,6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => 10111111111 => [1,2,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => 1011111110 => [1,2,1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,2,5] => 111010000 => [1,1,1,2,5]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,2,4] => 111101000 => [1,1,1,1,2,4]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,2,3] => 111110100 => [1,1,1,1,1,2,3]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,2,2] => 111111010 => [1,1,1,1,1,1,2,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,2] => 10000000010 => [1,9,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,1,1,1] => 1000100111 => [1,4,3,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,1,1,1] => 110010111 => [1,1,3,2,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1,1,1] => 1010001111 => [1,2,4,1,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,5,1,1,1] => 1010000111 => [1,2,5,1,1,1]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,7,1] => 1110000001 => [1,1,1,7,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,6,1] => 1111000001 => [1,1,1,1,6,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [7,3] => 1000000100 => [1,7,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [8,2] => 1000000010 => [1,8,2]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5] => 110010000 => [1,1,3,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,1,2] => 100001110 => [1,5,1,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [2,1,4,1,1,1] => 1011000111 => [1,2,1,4,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,3,1,1] => 111110011 => [1,1,1,1,1,3,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,1,2,1,1] => 110111011 => [1,1,2,1,1,2,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,3,1,1,1,1] => 111001111 => [1,1,1,3,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,2,2,1,1,1] => 111010111 => [1,1,1,2,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1,1] => 1011011111 => [1,2,1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 110111111 => [1,1,2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,1,1,2] => 1001111110 => [1,3,1,1,1,1,1,2]
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,4,1,1,2] => 110001110 => [1,1,4,1,1,2]
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,4,1,2] => 111000110 => [1,1,1,4,1,2]
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,4,2] => 111100010 => [1,1,1,1,4,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,1,3,1] => 11111111001 => [1,1,1,1,1,1,1,1,3,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,2,1] => 11111111101 => [1,1,1,1,1,1,1,1,1,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => 111001111 => [1,1,1,3,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,1,3,1] => 100111001 => [1,3,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,2,1,1] => 111111011 => [1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,1,2] => 111101110 => [1,1,1,1,2,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,2,1,1] => 1111111011 => [1,1,1,1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 101111110 => [1,2,1,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,1,2] => 110111110 => [1,1,2,1,1,1,1,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,1,2] => 111011110 => [1,1,1,2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => 1101111111 => [1,1,2,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1,1,1] => 1110111111 => [1,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,1,2] => 1110111110 => [1,1,1,2,1,1,1,1,2]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,1,2] => 1101111110 => [1,1,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => 1011111110 => [1,2,1,1,1,1,1,1,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,5,2] => 111000010 => [1,1,1,5,2]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,4,2] => 110100010 => [1,1,2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,9,1] => 11000000001 => [1,1,9,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => 10111111111 => [1,2,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,2,1,1,1] => 101010111 => [1,2,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,5,1] => 101100001 => [1,2,1,5,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,2,1,3] => 101101100 => [1,2,1,2,1,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => 101011110 => [1,2,2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1,1] => 110111111 => [1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,1,2,1,1] => 111011011 => [1,1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,1,2,1] => 110111101 => [1,1,2,1,1,1,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,1,1,3] => 1000111100 => [1,4,1,1,1,3]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,1,1,4] => 1000111000 => [1,4,1,1,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,1,3] => 100111100 => [1,3,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,1,5] => 1001110000 => [1,3,1,1,5]
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,1,4] => 100111000 => [1,3,1,1,4]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => 101110000 => [1,2,1,1,5]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,2] => 1000000010 => [1,8,2]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,5] => 1000010000 => [1,5,5]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,6] => 1000100000 => [1,4,6]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,7] => 1001000000 => [1,3,7]
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,1,4] => 111011000 => [1,1,1,2,1,4]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,2,4,1] => 111010001 => [1,1,1,2,4,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,2,4,1] => 111010001 => [1,1,1,2,4,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [2,7,1] => 1010000001 => [1,2,7,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [6,3,1] => 1000001001 => [1,6,3,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,1,3,1] => 101111001 => [1,2,1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1,1,1] => 1011011111 => [1,2,1,2,1,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1,1,1] => 1000101111 => [1,4,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1,1,1] => 1001001111 => [1,3,3,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,2,1,1] => 110111011 => [1,1,2,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,2,2,1] => 111110101 => [1,1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,2,2,1,1] => 111101011 => [1,1,1,1,2,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1,1] => 111010111 => [1,1,1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1,1] => 110101111 => [1,1,2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,1,3,1] => 100111001 => [1,3,1,1,3,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => 1011111110 => [1,2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [4,2,1,2] => 100010110 => [1,4,2,1,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1,1] => 10000011111 => [1,6,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,1,1,2,1] => 1000111101 => [1,4,1,1,1,2,1]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,5] => 1000110000 => [1,4,1,5]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [2,3,2,1,1] => 101001011 => [1,2,3,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,5,1] => 110100001 => [1,1,2,5,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,1,4,1] => 110110001 => [1,1,2,1,4,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,1,3,1] => 110111001 => [1,1,2,1,1,3,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,2,1,1,1] => 101010111 => [1,2,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2,2] => 11010101010 => [1,1,2,2,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,1,2,2] => 100111010 => [1,3,1,1,2,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 100110101 => [1,3,1,2,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2,2] => 1001101010 => [1,3,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,2,2,1] => 10101010101 => [1,2,2,2,2,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1,1,1,1] => 10000011111 => [1,6,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1,1] => 1000100111 => [1,4,3,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,2,1,1,1,1] => 10000101111 => [1,5,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,4] => 100101000 => [1,3,2,4]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,2,2,1] => 111110101 => [1,1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,2,3,1] => 111101001 => [1,1,1,1,2,3,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,2,4,1] => 111010001 => [1,1,1,2,4,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1,1,1,1] => 11001111111 => [1,1,3,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,1,5] => 110110000 => [1,1,2,1,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => 101110100 => [1,2,1,1,2,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,1,3,2] => 101110010 => [1,2,1,1,3,2]
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,4,1,4] => 1100011000 => [1,1,4,1,4]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,1,4,1] => 101110001 => [1,2,1,1,4,1]
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,1,5] => 1100110000 => [1,1,3,1,5]
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,1,6] => 1101100000 => [1,1,2,1,6]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,2,2,1] => 111110101 => [1,1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => 111101111 => [1,1,1,1,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => 1101111111 => [1,1,2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => 110101111 => [1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1] => 111010111 => [1,1,1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,2,2,1,1] => 111101011 => [1,1,1,1,2,2,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1,1,1] => 1101111111 => [1,1,2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => 1101111111 => [1,1,2,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1,1] => 1110111111 => [1,1,1,2,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,4,1,1] => 101100011 => [1,2,1,4,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,3,2] => 111110010 => [1,1,1,1,1,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,2,2] => 1111111010 => [1,1,1,1,1,1,1,2,2]
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,4,3] => 111000100 => [1,1,1,4,3]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,4,2] => 111100010 => [1,1,1,1,4,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,2,3,1,1] => 101010011 => [1,2,2,3,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [5,1,1,2,1] => 1000011101 => [1,5,1,1,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,1,2,1,1] => 1000011011 => [1,5,1,2,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,2,1,1,1] => 1000010111 => [1,5,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,5,3] => 110000100 => [1,1,5,3]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1] => 110110111 => [1,1,2,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,1,1,1,2] => 1000011110 => [1,5,1,1,1,2]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,1,2,1] => 110111101 => [1,1,2,1,1,1,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => 111011111 => [1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1,1] => 111001111 => [1,1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => 111101111 => [1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,3,1,1,1] => 111100111 => [1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,3,1,1,1,1] => 1111001111 => [1,1,1,1,3,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1,1,1] => 1110111111 => [1,1,1,2,1,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1,1] => 110101111 => [1,1,2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,1,1,1] => 110010111 => [1,1,3,2,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1,1,1] => 1110011111 => [1,1,1,3,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,9,1] => 11000000001 => [1,1,9,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0] => [4,2,3] => 100010100 => [1,4,2,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,2] => 110001010 => [1,1,4,2,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => 100011010 => [1,4,1,2,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 10000011111 => [1,6,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,6,2] => 110000010 => [1,1,6,2]
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,2,1,1,3] => 111011100 => [1,1,1,2,1,1,3]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => 101110001 => [1,2,1,1,4,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => 101110001 => [1,2,1,1,4,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,1,1,2] => 1101111110 => [1,1,2,1,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => 110111110 => [1,1,2,1,1,1,1,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,2,1,1,1] => 1111010111 => [1,1,1,1,2,2,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1,1] => 110100111 => [1,1,2,3,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [7,1,2] => 1000000110 => [1,7,1,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 100110101 => [1,3,1,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => 100101101 => [1,3,2,1,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2,2] => 1001101010 => [1,3,1,2,2,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => 100101101 => [1,3,2,1,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,2,2] => 1001011010 => [1,3,2,1,2,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,2,1,2] => 1001010110 => [1,3,2,2,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,2,1] => 1001010101 => [1,3,2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,2,1] => 1001010101 => [1,3,2,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => 1001010101 => [1,3,2,2,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => 1001010101 => [1,3,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [2,3,2,1,1] => 101001011 => [1,2,3,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,4,1,1] => 101100011 => [1,2,1,4,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,4,1,1] => 101100011 => [1,2,1,4,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => 101110100 => [1,2,1,1,2,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,2,3,1] => 111101001 => [1,1,1,1,2,3,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,5,1] => 110100001 => [1,1,2,5,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,1,2,1] => 110111101 => [1,1,2,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 101111110 => [1,2,1,1,1,1,1,2]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1,1] => 1110101111 => [1,1,1,2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1,1] => 1101101111 => [1,1,2,1,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,1,1,1,1] => 1100001111 => [1,1,5,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,4,1,1,1] => 111000111 => [1,1,1,4,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [2,5,1,1,1] => 1010000111 => [1,2,5,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [2,1,4,1,1,1] => 1011000111 => [1,2,1,4,1,1,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [3,1,4,1,1] => 1001100011 => [1,3,1,4,1,1]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,1,1,3,1] => 1000111001 => [1,4,1,1,3,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,1,1,2,1] => 1000111101 => [1,4,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1,1] => 111011111 => [1,1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => 101111101 => [1,2,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1,1] => 1011110111 => [1,2,1,1,1,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1,1,1] => 1011011111 => [1,2,1,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => 101110000 => [1,2,1,1,5]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,5,1] => 101100001 => [1,2,1,5,1]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [7,3] => 1000000100 => [1,7,3]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [6,2,1] => 100000101 => [1,6,2,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,7,2] => 1100000010 => [1,1,7,2]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,2,1,1,1] => 1000010111 => [1,5,2,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,3,1,1] => 111110011 => [1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1,1] => 111100111 => [1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,4,1,1] => 111100011 => [1,1,1,1,4,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,3,1,1] => 1111110011 => [1,1,1,1,1,1,3,1,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [3,3,3] => 100100100 => [1,3,3,3]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,2,1,1] => 100001011 => [1,5,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [5,3,1] => 100001001 => [1,5,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,1,2,1] => 110111101 => [1,1,2,1,1,1,2,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,5,1] => 100100001 => [1,3,5,1]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,6] => 1000100000 => [1,4,6]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,4,3] => 101000100 => [1,2,4,3]
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => 101001000 => [1,2,3,4]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [2,3,3,1] => 101001001 => [1,2,3,3,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,3,2,1] => 100100101 => [1,3,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,1,1,2] => 1101111110 => [1,1,2,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [6,3,1] => 1000001001 => [1,6,3,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,2,3,1] => 110101001 => [1,1,2,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,3,2,1] => 110100101 => [1,1,2,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,2,1] => 110010101 => [1,1,3,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,2,3,1] => 1010101001 => [1,2,2,2,3,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,3,2,1] => 110100101 => [1,1,2,3,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,2,3,2,1] => 1010100101 => [1,2,2,3,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,3,2,2,1] => 110010101 => [1,1,3,2,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,2,1] => 1010010101 => [1,2,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,2,2,2,1] => 111010101 => [1,1,1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1,1] => 1110011111 => [1,1,1,3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,4,1] => 111110001 => [1,1,1,1,1,4,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,4,1,1] => 111100011 => [1,1,1,1,4,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,1,3] => 100011100 => [1,4,1,1,3]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1,1] => 110101111 => [1,1,2,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [4,2,1,1,1,1] => 1000101111 => [1,4,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1] => 101010111 => [1,2,2,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,2,1,1,1] => 1000110111 => [1,4,1,2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,1,3,1,1] => 1000110011 => [1,4,1,3,1,1]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,1,2,1] => 1000001101 => [1,6,1,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,1,1,1] => 110100111 => [1,1,2,3,1,1,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,1,3,1] => 101111001 => [1,2,1,1,1,3,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,2,2,1,1,1] => 111010111 => [1,1,1,2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1,1] => 10000011111 => [1,6,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1,1] => 110101111 => [1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,2,1,1,1] => 111010111 => [1,1,1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,2,2,1,1] => 111101011 => [1,1,1,1,2,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,2,2,1] => 111110101 => [1,1,1,1,1,2,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,1,1,3,2,1] => 1011100101 => [1,2,1,1,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,3,2,1] => 111100101 => [1,1,1,1,3,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,2,2,2,1] => 111010101 => [1,1,1,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,3,1,1,1] => 110100111 => [1,1,2,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => 110010111 => [1,1,3,2,1,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,2,3,1,1,1] => 1010100111 => [1,2,2,3,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,2,1,1,1] => 110110111 => [1,1,2,1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 110111111 => [1,1,2,1,1,1,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [2,2,1,2,2] => 101011010 => [1,2,2,1,2,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2,2] => 101101010 => [1,2,1,2,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,2,1,1,1] => 101010111 => [1,2,2,2,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,2,1,2,1] => 1010101101 => [1,2,2,2,1,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,3,1,2] => 101100110 => [1,2,1,3,1,2]
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,2,1] => 1010110101 => [1,2,2,1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,1,2,2] => 110011010 => [1,1,3,1,2,2]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,2,2,2,1] => 1011010101 => [1,2,1,2,2,2,1]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => 1001010101 => [1,3,2,2,2,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,5,1] => 110100001 => [1,1,2,5,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => 111011110 => [1,1,1,2,1,1,1,2]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [3,2,4] => 100101000 => [1,3,2,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,2,1,2] => 111110110 => [1,1,1,1,1,2,1,2]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,4,2] => 110100010 => [1,1,2,4,2]
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,3,2] => 110010010 => [1,1,3,3,2]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1,1] => 1001011111 => [1,3,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,5,1,2] => 110000110 => [1,1,5,1,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,5,1,1] => 111000011 => [1,1,1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1,1] => 110000111 => [1,1,5,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [2,4,1,2] => 101000110 => [1,2,4,1,2]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,6,1,2] => 1100000110 => [1,1,6,1,2]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,1,1,2,1,1] => 1001111011 => [1,3,1,1,1,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1,1] => 1001011111 => [1,3,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,1,1,1,2] => 10011111110 => [1,3,1,1,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,1,1,3] => 1001111100 => [1,3,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,1,1,3,1] => 1001111001 => [1,3,1,1,1,3,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,3,3,1] => 111001001 => [1,1,1,3,3,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,1,3,1] => 100011001 => [1,4,1,3,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,1,3,2] => 110110010 => [1,1,2,1,3,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,3,2,2] => 111001010 => [1,1,1,3,2,2]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2,2] => 1100101010 => [1,1,3,2,2,2]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,3,2,2] => 1101001010 => [1,1,2,3,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,2,3,2] => 1101010010 => [1,1,2,2,3,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,3,1,2] => 110100110 => [1,1,2,3,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 101111000 => [1,2,1,1,1,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1,1] => 1011110111 => [1,2,1,1,1,2,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,2,2,2] => 111101010 => [1,1,1,1,2,2,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,3,1,2] => 111100110 => [1,1,1,1,3,1,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,2,2,2] => 1111101010 => [1,1,1,1,1,2,2,2]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,2,2,2,1] => 1111010101 => [1,1,1,1,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,4,1,2] => 111000110 => [1,1,1,4,1,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,1,2,2] => 111011010 => [1,1,1,2,1,2,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,1,2] => 111001110 => [1,1,1,3,1,1,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,4,1,2] => 111000110 => [1,1,1,4,1,2]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,7,1] => 1010000001 => [1,2,7,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1,1] => 111001111 => [1,1,1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1,1,1] => 1100111111 => [1,1,3,1,1,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1,1,1] => 1110011111 => [1,1,1,3,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,1,2,1,1] => 1001111011 => [1,3,1,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,2,1,1] => 110111011 => [1,1,2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,2,1,1] => 111011011 => [1,1,1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,2,1] => 110111101 => [1,1,2,1,1,1,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,1,1,2,1] => 10111111101 => [1,2,1,1,1,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,1,1,2] => 1001111110 => [1,3,1,1,1,1,1,2]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1,1] => 1001011111 => [1,3,2,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,2,1,3] => 101101100 => [1,2,1,2,1,3]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,4,1,2] => 101000110 => [1,2,4,1,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,3,1,3] => 101001100 => [1,2,3,1,3]
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => 101011000 => [1,2,2,1,4]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,3,1,3] => 111001100 => [1,1,1,3,1,3]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,5,1,2] => 110000110 => [1,1,5,1,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,4,1,3] => 110001100 => [1,1,4,1,3]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,1,4] => 110011000 => [1,1,3,1,4]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,1,3,1,1] => 101110011 => [1,2,1,1,3,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,1,2,2] => 1000111010 => [1,4,1,1,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,2,2] => 1010011010 => [1,2,3,1,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,4,1,1,2] => 1010001110 => [1,2,4,1,1,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,3,1,1,2] => 1001001110 => [1,3,3,1,1,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,2,1,1,2] => 1000101110 => [1,4,2,1,1,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,1,1,2] => 1000011110 => [1,5,1,1,1,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,2,3,1,2] => 1010100110 => [1,2,2,3,1,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,3,1,2] => 1001100110 => [1,3,1,3,1,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,1,2,1,2] => 1000110110 => [1,4,1,2,1,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,3,2,1,2] => 1010010110 => [1,2,3,2,1,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,2,4,1,1] => 1010100011 => [1,2,2,4,1,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,4,1,1] => 1001100011 => [1,3,1,4,1,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,1,3,1,1] => 1000110011 => [1,4,1,3,1,1]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,3,1,1] => 1010010011 => [1,2,3,3,1,1]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,3,1,1] => 1001010011 => [1,3,2,3,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,2,1,1] => 1000101011 => [1,4,2,2,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,1,2,1,1] => 1000011011 => [1,5,1,2,1,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,1,1,1] => 1000100111 => [1,4,3,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,2,1,1,1] => 1000010111 => [1,5,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,4,2,1,1] => 1010001011 => [1,2,4,2,1,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,3,2,1,1] => 1001001011 => [1,3,3,2,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,5,1,1,1] => 1010000111 => [1,2,5,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,4,1,1,1] => 1001000111 => [1,3,4,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,2,3,1] => 1001101001 => [1,3,1,2,3,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,1,1,3,1] => 1000111001 => [1,4,1,1,3,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,3,1] => 1010011001 => [1,2,3,1,3,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,1,3,1] => 1001011001 => [1,3,2,1,3,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,4,1,2,1] => 1010001101 => [1,2,4,1,2,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,3,1,2,1] => 1001001101 => [1,3,3,1,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,2,1,2,1] => 1000101101 => [1,4,2,1,2,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,1,1,2,1] => 1000011101 => [1,5,1,1,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,3,2,1] => 1001100101 => [1,3,1,3,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,1,2,2,1] => 1000110101 => [1,4,1,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,2,2,2] => 100101101010 => [1,3,2,1,2,2,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,3,1,1,2,2] => 100100111010 => [1,3,3,1,1,2,2]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,1,1,1,2] => 100010011110 => [1,4,3,1,1,1,2]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,3,2,1,1,2] => 100100101110 => [1,3,3,2,1,1,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2,3,1,2] => 100110100110 => [1,3,1,2,3,1,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,1,1,3,1,2] => 100011100110 => [1,4,1,1,3,1,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,2,1,2,1,2] => 100010110110 => [1,4,2,1,2,1,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,3,2,1,2] => 101010010110 => [1,2,2,3,2,1,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,2,2,1,2] => 100101010110 => [1,3,2,2,2,1,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,2,4,1,1] => 100110100011 => [1,3,1,2,4,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1,4,1,1] => 100011100011 => [1,4,1,1,4,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,2,1,3,1,1] => 100010110011 => [1,4,2,1,3,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,2,3,3,1,1] => 101010010011 => [1,2,2,3,3,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,2,3,1,1] => 100101010011 => [1,3,2,2,3,1,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,3,2,2,1,1] => 100100101011 => [1,3,3,2,2,1,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,1,2,1,1] => 100010011011 => [1,4,3,1,2,1,1]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [4,4,1,1,1,1] => 100010001111 => [1,4,4,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,2,2,3,1] => 101010101001 => [1,2,2,2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,3,2,1] => 101010100101 => [1,2,2,2,3,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,3,2,2,1] => 101010010101 => [1,2,2,3,2,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,2,2,1] => 101001010101 => [1,2,3,2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,2,2,1] => 100101010101 => [1,3,2,2,2,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => 101111001 => [1,2,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,1,3,1,1] => 101110011 => [1,2,1,1,3,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1,1] => 1011110111 => [1,2,1,1,1,2,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1,1,1] => 1011011111 => [1,2,1,2,1,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => 10111111111 => [1,2,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,1,1,1,2,1] => 10111111101 => [1,2,1,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,1,3,1,1] => 101110011 => [1,2,1,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => 101110001 => [1,2,1,1,4,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,4,1,1] => 101100011 => [1,2,1,4,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1,1,1] => 1100111111 => [1,1,3,1,1,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => 100101101 => [1,3,2,1,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,1,2,2] => 110111010 => [1,1,2,1,1,2,2]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,1,2,2] => 110011010 => [1,1,3,1,2,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,1,2,2] => 101111010 => [1,2,1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,2,1,2,2] => 101011010 => [1,2,2,1,2,2]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,1,2,2] => 1000111010 => [1,4,1,1,2,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2,2] => 1000101010 => [1,4,2,2,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0] => [6,2,2] => 1000001010 => [1,6,2,2]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 1000101111 => [1,4,2,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [4,1,2,1,1,1] => 1000110111 => [1,4,1,2,1,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,1,1,2,1,1] => 1000111011 => [1,4,1,1,2,1,1]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,1,2,1] => 110011101 => [1,1,3,1,1,2,1]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [4,1,3,1,1] => 1000110011 => [1,4,1,3,1,1]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [4,3,1,1,1] => 1000100111 => [1,4,3,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,4,1] => 100010001 => [1,4,4,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 101111000 => [1,2,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1] => 100000000001 => [1,11,1]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => [11,1] => 100000000001 => [1,11,1]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [6,3,1] => 1000001001 => [1,6,3,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,2,1] => 100010101 => [1,4,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,2,1] => 10101010101 => [1,2,2,2,2,2,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => 1000101010 => [1,4,2,2,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,2,1] => 100010101 => [1,4,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,1,2,1] => 101011101 => [1,2,2,1,1,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,2,1] => 10101010101 => [1,2,2,2,2,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,1,1,2] => 1001111110 => [1,3,1,1,1,1,1,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,1,2] => 110011110 => [1,1,3,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [2,6,2] => 1010000010 => [1,2,6,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,1,1,2] => 1000111110 => [1,4,1,1,1,1,2]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,1,1,1,1,2] => 10000111110 => [1,5,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => 101100001 => [1,2,1,5,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 100110001 => [1,3,1,4,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 100011001 => [1,4,1,3,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,6,1] => 1011000001 => [1,2,1,6,1]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 100110001 => [1,3,1,4,1]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,5,1] => 1001100001 => [1,3,1,5,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 100011001 => [1,4,1,3,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,1,4,1] => 110110001 => [1,1,2,1,4,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,4,1] => 1000110001 => [1,4,1,4,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,1,3,1] => 110011001 => [1,1,3,1,3,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,1,3,1] => 1000011001 => [1,5,1,3,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,4,1,2,1] => 110001101 => [1,1,4,1,2,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,1,2,1] => 1000001101 => [1,6,1,2,1]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [2,5,1,1,1] => 1010000111 => [1,2,5,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1,1] => 1010001111 => [1,2,4,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,1,1,2] => 1001111110 => [1,3,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 101111011 => [1,2,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,4,1,2,1] => 110001101 => [1,1,4,1,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,3,2,2,1,1] => 1100101011 => [1,1,3,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,1,3,2,1] => 1101100101 => [1,1,2,1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,2,3,2,1,1] => 1101001011 => [1,1,2,3,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,4,2,1,1,1] => 1100010111 => [1,1,4,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,2,1,3,1] => 1101011001 => [1,1,2,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,1,3,1,1] => 1100110011 => [1,1,3,1,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,1,1,2] => 1101001110 => [1,1,2,3,1,1,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,4,1,1,2,1] => 1100011101 => [1,1,4,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,2,3,1,1] => 1101010011 => [1,1,2,2,3,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,3,3,1,1,1] => 1100100111 => [1,1,3,3,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,4,1,1] => 1101100011 => [1,1,2,1,4,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,2,4,1,1,1] => 1101000111 => [1,1,2,4,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,5,1,1,1,1] => 1100001111 => [1,1,5,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1,2,1] => 1100101101 => [1,1,3,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,1,3,1,2] => 1101100110 => [1,1,2,1,3,1,2]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,2,3,1,2,1] => 1101001101 => [1,1,2,3,1,2,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,4,1,2,1,1] => 1100011011 => [1,1,4,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,2,1,2,2] => 1101011010 => [1,1,2,2,1,2,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,1,2,2,1] => 1100110101 => [1,1,3,1,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,1,1,3,1] => 1100111001 => [1,1,3,1,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,3,2,1,2,1] => 1100101101 => [1,1,3,2,1,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,3,1,2,1] => 1101001101 => [1,1,2,3,1,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,1,2,1,1] => 1100011011 => [1,1,4,1,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,3,2,2,1,1] => 1100101011 => [1,1,3,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,1,3,2,1] => 1101100101 => [1,1,2,1,3,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,2,3,2,1,1] => 1101001011 => [1,1,2,3,2,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,4,2,1,1,1] => 1100010111 => [1,1,4,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,2,1,3,1] => 1101011001 => [1,1,2,2,1,3,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,1,3,1,1] => 1100110011 => [1,1,3,1,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,2,3,1,1,2] => 1101001110 => [1,1,2,3,1,1,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,1,1,2,1] => 1100011101 => [1,1,4,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,2,3,1,1] => 1101010011 => [1,1,2,2,3,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,3,3,1,1,1] => 1100100111 => [1,1,3,3,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,1,4,1,1] => 1101100011 => [1,1,2,1,4,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,2,4,1,1,1] => 1101000111 => [1,1,2,4,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,5,1,1,1,1] => 1100001111 => [1,1,5,1,1,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [1,3,2,2,2,1,1] => 110010101011 => [1,1,3,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [1,2,3,2,2,1,1] => 110100101011 => [1,1,2,3,2,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [1,4,2,2,1,1,1] => 110001010111 => [1,1,4,2,2,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,3,1,3,2,1,1] => 110011001011 => [1,1,3,1,3,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,1,1,2,1] => 110001011101 => [1,1,4,2,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => [1,2,2,3,2,1,1] => 110101001011 => [1,1,2,2,3,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => [1,3,3,2,1,1,1] => 110010010111 => [1,1,3,3,2,1,1,1]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [1,2,4,2,1,1,1] => 110100010111 => [1,1,2,4,2,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => [1,5,2,1,1,1,1] => 110000101111 => [1,1,5,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,3,2,1,3,1,1] => 110010110011 => [1,1,3,2,1,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,2,3,1,3,1,1] => 110100110011 => [1,1,2,3,1,3,1,1]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,4,1,3,1,1,1] => 110001100111 => [1,1,4,1,3,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,2,1,2,3,1] => 110101101001 => [1,1,2,2,1,2,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,1,2,3,1,1] => 110011010011 => [1,1,3,1,2,3,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0] => [1,3,3,1,1,2,1] => 110010011101 => [1,1,3,3,1,1,2,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,4,1,1,2,1] => 110100011101 => [1,1,2,4,1,1,2,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1,1,2,1,1] => 110000111011 => [1,1,5,1,1,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,2,2,3,1,1] => 110101010011 => [1,1,2,2,2,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [1,3,2,3,1,1,1] => 110010100111 => [1,1,3,2,3,1,1,1]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [1,2,3,3,1,1,1] => 110100100111 => [1,1,2,3,3,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => [1,4,3,1,1,1,1] => 110001001111 => [1,1,4,3,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,2,1,4,1,1] => 110101100011 => [1,1,2,2,1,4,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,3,1,4,1,1,1] => 110011000111 => [1,1,3,1,4,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,5,1,1,1,2,1] => 110000111101 => [1,1,5,1,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => [1,2,2,4,1,1,1] => 110101000111 => [1,1,2,2,4,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => [1,3,4,1,1,1,1] => 110010001111 => [1,1,3,4,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,2,5,1,1,1,1] => 110100001111 => [1,1,2,5,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1,1,1,1,1] => 110000011111 => [1,1,6,1,1,1,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0] => [1,3,2,2,1,2,1] => 110010101101 => [1,1,3,2,2,1,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0] => [1,2,3,2,1,2,1] => 110100101101 => [1,1,2,3,2,1,2,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,4,2,1,2,1,1] => 110001011011 => [1,1,4,2,1,2,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,3,1,2,1] => 110011001101 => [1,1,3,1,3,1,2,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,4,1,2,1,2,1] => 110001101101 => [1,1,4,1,2,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [1,2,2,3,1,2,1] => 110101001101 => [1,1,2,2,3,1,2,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,3,3,1,2,1,1] => 110010011011 => [1,1,3,3,1,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,2,4,1,2,1,1] => 110100011011 => [1,1,2,4,1,2,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,5,1,2,1,1,1] => 110000110111 => [1,1,5,1,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1,2,2,1] => 110010110101 => [1,1,3,2,1,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,2,3,1,2,2,1] => 110100110101 => [1,1,2,3,1,2,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,4,1,2,2,1,1] => 110001101011 => [1,1,4,1,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1,3,1,1] => 110001110011 => [1,1,4,1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,1,2,2,1] => 110010110101 => [1,1,3,2,1,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,1,2,1,3,1] => 110011011001 => [1,1,3,1,2,1,3,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,1,2,2,1] => 110100110101 => [1,1,2,3,1,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,4,1,2,2,1,1] => 110001101011 => [1,1,4,1,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1,1,3,1,1] => 110001110011 => [1,1,4,1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0] => [1,3,2,2,1,2,1] => 110010101101 => [1,1,3,2,2,1,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0] => [1,2,3,2,1,2,1] => 110100101101 => [1,1,2,3,2,1,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,4,2,1,2,1,1] => 110001011011 => [1,1,4,2,1,2,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,3,1,2,1] => 110011001101 => [1,1,3,1,3,1,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,1,2,1,2,1] => 110001101101 => [1,1,4,1,2,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [1,2,2,3,1,2,1] => 110101001101 => [1,1,2,2,3,1,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,3,3,1,2,1,1] => 110010011011 => [1,1,3,3,1,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,2,4,1,2,1,1] => 110100011011 => [1,1,2,4,1,2,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,1,2,1,1,1] => 110000110111 => [1,1,5,1,2,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,2,2,2,2,2,1] => 110101010101 => [1,1,2,2,2,2,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [1,3,2,2,2,1,1] => 110010101011 => [1,1,3,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [1,2,3,2,2,1,1] => 110100101011 => [1,1,2,3,2,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => [1,4,2,2,1,1,1] => 110001010111 => [1,1,4,2,2,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,3,1,3,2,1,1] => 110011001011 => [1,1,3,1,3,2,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,1,1,2,1] => 110001011101 => [1,1,4,2,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0] => [1,2,2,3,2,1,1] => 110101001011 => [1,1,2,2,3,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0] => [1,3,3,2,1,1,1] => 110010010111 => [1,1,3,3,2,1,1,1]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [1,2,4,2,1,1,1] => 110100010111 => [1,1,2,4,2,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,5,2,1,1,1,1] => 110000101111 => [1,1,5,2,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,3,2,1,3,1,1] => 110010110011 => [1,1,3,2,1,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,2,3,1,3,1,1] => 110100110011 => [1,1,2,3,1,3,1,1]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,4,1,3,1,1,1] => 110001100111 => [1,1,4,1,3,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,2,1,2,3,1] => 110101101001 => [1,1,2,2,1,2,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,1,2,3,1,1] => 110011010011 => [1,1,3,1,2,3,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,3,3,1,1,2,1] => 110010011101 => [1,1,3,3,1,1,2,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,2,4,1,1,2,1] => 110100011101 => [1,1,2,4,1,1,2,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1,1,2,1,1] => 110000111011 => [1,1,5,1,1,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,2,2,2,3,1,1] => 110101010011 => [1,1,2,2,2,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [1,3,2,3,1,1,1] => 110010100111 => [1,1,3,2,3,1,1,1]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => [1,2,3,3,1,1,1] => 110100100111 => [1,1,2,3,3,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [1,4,3,1,1,1,1] => 110001001111 => [1,1,4,3,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,2,1,4,1,1] => 110101100011 => [1,1,2,2,1,4,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,3,1,4,1,1,1] => 110011000111 => [1,1,3,1,4,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,5,1,1,1,2,1] => 110000111101 => [1,1,5,1,1,1,2,1]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,2,2,4,1,1,1] => 110101000111 => [1,1,2,2,4,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [1,3,4,1,1,1,1] => 110010001111 => [1,1,3,4,1,1,1,1]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,2,5,1,1,1,1] => 110100001111 => [1,1,2,5,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1,1,1,1,1] => 110000011111 => [1,1,6,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,1,2] => 1001111110 => [1,3,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [6,2,1,1] => 1000001011 => [1,6,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [5,2,1,1,1] => 1000010111 => [1,5,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [4,2,1,1,1,1] => 1000101111 => [1,4,2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1,1] => 1001011111 => [1,3,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,1,1,2] => 1000001110 => [1,6,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,1,1,2] => 11011111110 => [1,1,2,1,1,1,1,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,1,2,1] => 1101111101 => [1,1,2,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,1,2,1,1] => 110111011 => [1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,1,3] => 110111100 => [1,1,2,1,1,1,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,1,1,2,1] => 1101111101 => [1,1,2,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,1,2,1,1] => 110111011 => [1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,1,1,2,1] => 1101111101 => [1,1,2,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,1,1,1,2] => 11011111110 => [1,1,2,1,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,2,1,2] => 101010110 => [1,2,2,2,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [3,2,1,2,1] => 100101101 => [1,3,2,1,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,2,1,1,1] => 101010111 => [1,2,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,2,1] => 100110101 => [1,3,1,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,2,1,2,1] => 1010101101 => [1,2,2,2,1,2,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 100110101 => [1,3,1,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,1,2,1] => 111011101 => [1,1,1,2,1,1,2,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,2,4,1,1] => 110100011 => [1,1,2,4,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,1] => 100010011 => [1,4,3,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1,1] => 1100000111 => [1,1,6,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,6,1,1] => 1110000011 => [1,1,1,6,1,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,7,1,1] => 1100000011 => [1,1,7,1,1]
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,6,2] => 1110000010 => [1,1,1,6,2]
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,8,1] => 11100000001 => [1,1,1,8,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => 101000100 => [1,2,4,3]
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,1,5] => 1000110000 => [1,4,1,5]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0] => [7,1,2] => 1000000110 => [1,7,1,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0] => [9,2] => 10000000010 => [1,9,2]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [6,2,2] => 1000001010 => [1,6,2,2]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [6,2,1,1] => 1000001011 => [1,6,2,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => 101011111 => [1,2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [9,2] => 10000000010 => [1,9,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,2,2] => 1001011010 => [1,3,2,1,2,2]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,2,1] => 1001010101 => [1,3,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,3,2,2] => 101001010 => [1,2,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,2,3,2] => 101010010 => [1,2,2,3,2]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,2,3,1] => 110101001 => [1,1,2,2,3,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,2,3,1,2] => 110100110 => [1,1,2,3,1,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,3,2] => 100110010 => [1,3,1,3,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,2,3,1,1] => 101010011 => [1,2,2,3,1,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [2,3,1,2,1,1] => 1010011011 => [1,2,3,1,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,1,1,3,1] => 1000111001 => [1,4,1,1,3,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,3,1,1,1] => 100011100111 => [1,4,1,1,3,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,1,2,1,1,1] => 101110111 => [1,2,1,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,2,3,1] => 111101001 => [1,1,1,1,2,3,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1,1,1,1] => 10000011111 => [1,6,1,1,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,4,2,2] => 110001010 => [1,1,4,2,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,3,2,2,2] => 1100101010 => [1,1,3,2,2,2]
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => 1011111110 => [1,2,1,1,1,1,1,1,2]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,1,1,2] => 1100011110 => [1,1,4,1,1,1,2]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,1,1,1,2] => 11000111110 => [1,1,4,1,1,1,1,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,1,2] => 110011110 => [1,1,3,1,1,1,2]
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,1,2] => 110101110 => [1,1,2,2,1,1,2]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,2,1,1,1] => 110010111 => [1,1,3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,4,2,1] => 101000101 => [1,2,4,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => 100011010 => [1,4,1,2,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,3,1,2] => 100100110 => [1,3,3,1,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,1,2] => 110010110 => [1,1,3,2,1,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,1,2,2,1] => 1100110101 => [1,1,3,1,2,2,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [3,2,2,2,1] => 1001010101 => [1,3,2,2,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [3,2,2,1,1,1] => 1001010111 => [1,3,2,2,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [2,3,2,2,1] => 1010010101 => [1,2,3,2,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [2,3,2,1,1,1] => 1010010111 => [1,2,3,2,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,4,2,1,1,1] => 1100010111 => [1,1,4,2,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,2,1,1] => 1001101011 => [1,3,1,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1,2,1] => 1001101101 => [1,3,1,2,1,2,1]
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [2,2,3,2,1] => 1010100101 => [1,2,2,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,3,2,1,1] => 1011001011 => [1,2,1,3,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [2,2,3,1,1,1] => 1010100111 => [1,2,2,3,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,3,3,1,1,1] => 1100100111 => [1,1,3,3,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,1,3,1,2,1] => 1011001101 => [1,2,1,3,1,2,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,2,4,1,1,1] => 1101000111 => [1,1,2,4,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,5,1,1,1] => 1110000111 => [1,1,1,5,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0] => [2,3,1,2,1,1] => 1010011011 => [1,2,3,1,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [2,3,1,1,2,1] => 1010011101 => [1,2,3,1,1,2,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,4,1,2,1,1] => 1100011011 => [1,1,4,1,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,4,1,1,2,1] => 1100011101 => [1,1,4,1,1,2,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,2,2,3,1] => 1010101001 => [1,2,2,2,3,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,2,3,1,1] => 1011010011 => [1,2,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,1,3,1,1] => 1100110011 => [1,1,3,1,3,1,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,1,4,1,1] => 1011100011 => [1,2,1,1,4,1,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,4,1,1] => 1101100011 => [1,1,2,1,4,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,3,2,2,1,1] => 1100101011 => [1,1,3,2,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,2,1] => 1011010101 => [1,2,1,2,2,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,2,3,2,1,1] => 1101001011 => [1,1,2,3,2,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,4,2,1,1] => 1110001011 => [1,1,1,4,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,2,1] => 1100110101 => [1,1,3,1,2,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,1,1] => 1000011011 => [1,5,1,2,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,1,3,2,1] => 1011100101 => [1,2,1,1,3,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,1,3,2,1] => 1101100101 => [1,1,2,1,3,2,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,2,2,3,1,1] => 1101010011 => [1,1,2,2,3,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,3,1,1] => 1000110011 => [1,4,1,3,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,2,4,1,1] => 1110100011 => [1,1,1,2,4,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,4,1,1] => 1001100011 => [1,3,1,4,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0] => [2,2,2,2,2,1,1] => 101010101011 => [1,2,2,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [2,2,2,2,1,2,1] => 101010101101 => [1,2,2,2,2,1,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => [1,3,2,2,2,1,1] => 110010101011 => [1,1,3,2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [1,3,2,2,1,2,1] => 110010101101 => [1,1,3,2,2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,2,2,3,1,1] => 101101010011 => [1,2,1,2,2,3,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,2,2,1] => 101101010101 => [1,2,1,2,2,2,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => [1,2,3,2,2,1,1] => 110100101011 => [1,1,2,3,2,2,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,4,2,2,1,1] => 111000101011 => [1,1,1,4,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [1,2,3,2,1,2,1] => 110100101101 => [1,1,2,3,2,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,2,3,1,1] => 110011010011 => [1,1,3,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,1,2,2,2,1] => 110011010101 => [1,1,3,1,2,2,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,2,1,1,1,1] => 100001101111 => [1,5,1,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [1,2,2,3,2,1,1] => 110101001011 => [1,1,2,2,3,2,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => [1,1,2,4,2,1,1] => 111010001011 => [1,1,1,2,4,2,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [1,2,2,3,1,2,1] => 110101001101 => [1,1,2,2,3,1,2,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,3,1,1,1,1] => 100011001111 => [1,4,1,3,1,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0] => [3,1,4,1,1,1,1] => 100110001111 => [1,3,1,4,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [2,1,5,1,1,1,1] => 101100001111 => [1,2,1,5,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,3,1,1] => 110100110011 => [1,1,2,3,1,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,1,2,2,1] => 110100110101 => [1,1,2,3,1,2,2,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,1,2,1,1] => 100010011011 => [1,4,3,1,2,1,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,1,1,1,1,1] => 100010011111 => [1,4,3,1,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,4,1,2,2,1] => 111000110101 => [1,1,1,4,1,2,2,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0] => [3,4,1,1,1,1,1] => 100100011111 => [1,3,4,1,1,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,1,1,1,1] => 101000011111 => [1,2,5,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1,2,1,1,1] => 100001110111 => [1,5,1,1,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0] => [5,1,1,1,2,1,1] => 100001111011 => [1,5,1,1,1,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0] => [5,1,1,1,1,2,1] => 100001111101 => [1,5,1,1,1,1,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,1,1] => 100010110011 => [1,4,2,1,3,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [4,2,1,2,1,1,1] => 100010110111 => [1,4,2,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,2,1,1,2,1,1] => 100010111011 => [1,4,2,1,1,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,2,1,1,1,2,1] => 100010111101 => [1,4,2,1,1,1,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,1,1,4,1,1] => 100011100011 => [1,4,1,1,4,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,2,2,2,3,1,1] => 110101010011 => [1,1,2,2,2,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,3,2,3,1,1] => 111001010011 => [1,1,1,3,2,3,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,3,1,1,1] => 100011100111 => [1,4,1,1,3,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,3,1,1,1] => 100101100111 => [1,3,2,1,3,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,2,2,4,1,1] => 111010100011 => [1,1,1,2,2,4,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [3,1,2,4,1,1] => 100110100011 => [1,3,1,2,4,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,1,1,4,1,1,1] => 100111000111 => [1,3,1,1,4,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,2,1,4,1,1,1] => 101011000111 => [1,2,2,1,4,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,2,2,2,2,1] => 110101010101 => [1,1,2,2,2,2,2,1]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0] => [3,3,2,2,1,1] => 100100101011 => [1,3,3,2,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [4,1,2,2,1,1,1] => 100011010111 => [1,4,1,2,2,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,2,3,2,2,1] => 111010010101 => [1,1,1,2,3,2,2,1]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [3,1,3,2,1,1,1] => 100110010111 => [1,3,1,3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [2,1,4,2,1,1,1] => 101100010111 => [1,2,1,4,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [3,3,1,2,1,1,1] => 100100110111 => [1,3,3,1,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [2,4,1,2,1,1,1] => 101000110111 => [1,2,4,1,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,5,1,2,1,1,1] => 110000110111 => [1,1,5,1,2,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,1,2,2,1,1] => 100011101011 => [1,4,1,1,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,1,2,1,2,1] => 100011101101 => [1,4,1,1,2,1,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,2,2,1,1] => 100101101011 => [1,3,2,1,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,2,1,2,1] => 100101101101 => [1,3,2,1,2,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,1,3,2,1,1] => 100111001011 => [1,3,1,1,3,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,2,1,3,2,1,1] => 101011001011 => [1,2,2,1,3,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [3,2,2,3,1,1] => 100101010011 => [1,3,2,2,3,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [3,1,2,3,1,1,1] => 100110100111 => [1,3,1,2,3,1,1,1]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [2,2,3,3,1,1] => 101010010011 => [1,2,2,3,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [2,1,3,3,1,1,1] => 101100100111 => [1,2,1,3,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [2,3,1,3,1,1,1] => 101001100111 => [1,2,3,1,3,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,4,1,3,1,1,1] => 110001100111 => [1,1,4,1,3,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,3,1,2,1] => 100111001101 => [1,3,1,1,3,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,3,1,2,1] => 101011001101 => [1,2,2,1,3,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [2,1,2,4,1,1,1] => 101101000111 => [1,2,1,2,4,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,3,1,4,1,1,1] => 110011000111 => [1,1,3,1,4,1,1,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,1,1,3,1,1] => 1001110011 => [1,3,1,1,3,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,1,3,1,1,1] => 1001100111 => [1,3,1,3,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,1,1,3] => 1001111100 => [1,3,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,1,1,4] => 1001111000 => [1,3,1,1,1,4]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,1,4,1] => 1001110001 => [1,3,1,1,4,1]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,1,4,1,1] => 1001100011 => [1,3,1,4,1,1]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,4,1,1,1] => 1001000111 => [1,3,4,1,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,3,1,2] => 101100110 => [1,2,1,3,1,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => 101011000 => [1,2,2,1,4]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [2,3,3,1,1] => 1010010011 => [1,2,3,3,1,1]
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => [2,3,2,2,1] => 1010010101 => [1,2,3,2,2,1]
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1] => 1010010001 => [1,2,3,4,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => [2,3,2,1,2] => 1010010110 => [1,2,3,2,1,2]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,3,2] => 1010010010 => [1,2,3,3,2]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [2,2,2,1,2,1] => 1010101101 => [1,2,2,2,1,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2,1,3] => 1010101100 => [1,2,2,2,1,3]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => [2,4,2,1,1] => 1010001011 => [1,2,4,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [2,2,3,1,1,1] => 1010100111 => [1,2,2,3,1,1,1]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0] => [2,4,2,1,1] => 1010001011 => [1,2,4,2,1,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [2,2,4,2] => 1010100010 => [1,2,2,4,2]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0] => [2,4,1,2,1] => 1010001101 => [1,2,4,1,2,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [2,2,3,2,1] => 1010100101 => [1,2,2,3,2,1]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [3,1,3,2,1] => 1001100101 => [1,3,1,3,2,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,3,3] => 1001100100 => [1,3,1,3,3]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,2,1,1] => 1001101011 => [1,3,1,2,2,1,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,4,2] => 1001100010 => [1,3,1,4,2]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,2,3,1] => 1001101001 => [1,3,1,2,3,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [4,1,1,3,1] => 1000111001 => [1,4,1,1,3,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,1,1,2,2] => 1000111010 => [1,4,1,1,2,2]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,2,1,3,1] => 1001011001 => [1,3,2,1,3,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,2,1,2,2] => 1001011010 => [1,3,2,1,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [4,2,1,1,2] => 1000101110 => [1,4,2,1,1,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0] => [3,2,1,1,1,2] => 1001011110 => [1,3,2,1,1,1,2]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,2,1,2] => 1000010110 => [1,5,2,1,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => [3,3,1,1,2] => 1001001110 => [1,3,3,1,1,2]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [4,3,1,1,1] => 1000100111 => [1,4,3,1,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,2,1,1] => 1000101011 => [1,4,2,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0] => [4,2,1,2,1] => 1000101101 => [1,4,2,1,2,1]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [4,3,2,1] => 1000100101 => [1,4,3,2,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [3,2,1,2,1,1] => 1001011011 => [1,3,2,1,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => [3,2,1,3,1] => 1001011001 => [1,3,2,1,3,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => [5,2,1,1,1] => 1000010111 => [1,5,2,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [3,3,1,1,1,1] => 1001001111 => [1,3,3,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0] => [6,1,2,1] => 1000001101 => [1,6,1,2,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 1000010111 => [1,5,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0] => [5,1,2,1,1] => 1000011011 => [1,5,1,2,1,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [3,3,2,1,1] => 1001001011 => [1,3,3,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [2,2,2,1,3,1,1] => 101010110011 => [1,2,2,2,1,3,1,1]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => [2,2,2,1,2,2,1] => 101010110101 => [1,2,2,2,1,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0] => [2,2,3,1,1,2,1] => 101010011101 => [1,2,2,3,1,1,2,1]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0] => [2,4,2,1,1,1,1] => 101000101111 => [1,2,4,2,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0] => [2,4,1,2,1,1,1] => 101000110111 => [1,2,4,1,2,1,1,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,0] => [2,2,3,2,1,1,1] => 101010010111 => [1,2,2,3,2,1,1,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,0] => [2,2,3,2,1,2] => 101010010110 => [1,2,2,3,2,1,2]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [3,1,2,2,1,2,1] => 100110101101 => [1,3,1,2,2,1,2,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [3,1,2,3,1,1,1] => 100110100111 => [1,3,1,2,3,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,1,1,2,2,1,1] => 100011101011 => [1,4,1,1,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,2,1,2,2,1,1] => 100101101011 => [1,3,2,1,2,2,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,1,1,2,2] => 100100111010 => [1,3,3,1,1,2,2]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [4,3,1,1,1,2] => 100010011110 => [1,4,3,1,1,1,2]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0,0] => [4,2,1,2,1,2] => 100010110110 => [1,4,2,1,2,1,2]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0] => [3,3,2,1,1,2] => 100100101110 => [1,3,3,2,1,1,2]
[1,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [4,3,1,2,1,1] => 100010011011 => [1,4,3,1,2,1,1]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [4,4,1,1,1,1] => 100010001111 => [1,4,4,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0] => [4,2,1,3,1,1] => 100010110011 => [1,4,2,1,3,1,1]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0,0] => [4,5,2,1] => 100010000101 => [1,4,5,2,1]
[1,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [3,2,1,3,1,1,1] => 100101100111 => [1,3,2,1,3,1,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [3,2,1,2,2,1,1] => 100101101011 => [1,3,2,1,2,2,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0] => [3,2,1,2,1,2,1] => 100101101101 => [1,3,2,1,2,1,2,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [3,3,1,1,2,1,1] => 100100111011 => [1,3,3,1,1,2,1,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [5,2,1,1,1,1,1] => 100001011111 => [1,5,2,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [5,1,2,1,1,1,1] => 100001101111 => [1,5,1,2,1,1,1,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0] => [3,3,2,1,1,1,1] => 100100101111 => [1,3,3,2,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,1,2,1] => 100101101 => [1,3,2,1,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,1,2,2] => 110011010 => [1,1,3,1,2,2]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,1,3,2] => 1100110010 => [1,1,3,1,3,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,1,3,2] => 1100110010 => [1,1,3,1,3,2]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2,1,2] => 1100110110 => [1,1,3,1,2,1,2]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,1,3,2] => 110110010 => [1,1,2,1,3,2]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,2,1] => 1100110101 => [1,1,3,1,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,1,1,2,2] => 1011111010 => [1,2,1,1,1,1,2,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0] => [6,3,1] => 1000001001 => [1,6,3,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0] => [10,1] => 10000000001 => [1,10,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,3,2,1,1] => 101001011 => [1,2,3,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 1010101010 => [1,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 101010101010 => [1,2,2,2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,2,2,2,1,1] => 110101011 => [1,1,2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,2,2,1,2,1] => 110101101 => [1,1,2,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,1,2,2,1] => 110110101 => [1,1,2,1,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,2,3,1,2] => 110100110 => [1,1,2,3,1,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,2,2,3,1] => 110101001 => [1,1,2,2,3,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,2,2,2,1,1] => 110101011 => [1,1,2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,2,2,1,3] => 110101100 => [1,1,2,2,1,3]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,1,3,1,1] => 110110011 => [1,1,2,1,3,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,1,2,2] => 1101011010 => [1,1,2,2,1,2,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,3,1,2,1] => 111001101 => [1,1,1,3,1,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,2,3,1,2,1] => 1101001101 => [1,1,2,3,1,2,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,3,2,1] => 110100101 => [1,1,2,3,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,3,2,1] => 110100101 => [1,1,2,3,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,1,2,1] => 100111101 => [1,3,1,1,1,2,1]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,1,2,1] => 101011101 => [1,2,2,1,1,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1,1] => 100101111 => [1,3,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,2,1,1,2] => 100101110 => [1,3,2,1,1,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,1,3] => 100101100 => [1,3,2,1,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,3,1,2,1] => 101001101 => [1,2,3,1,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,2,1,2,1,1] => 111011011 => [1,1,1,2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => 111011110 => [1,1,1,2,1,1,1,2]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,3] => 10001000100 => [1,4,4,3]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1,1] => 100000111 => [1,6,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,2,3,1,1,1] => 1010100111 => [1,2,2,3,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,2,1,1,1] => 1010010111 => [1,2,3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1,1] => 1010001111 => [1,2,4,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,2,1,1] => 1001101011 => [1,3,1,2,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,3,1,1,1] => 1001100111 => [1,3,1,3,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,2,1,1] => 1001011011 => [1,3,2,1,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,1,2,1,1] => 1000111011 => [1,4,1,1,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,2,1,1,1] => 1001010111 => [1,3,2,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [3,3,1,1,1,1] => 1001001111 => [1,3,3,1,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,2,1,1,1] => 1000110111 => [1,4,1,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,2,1,1,1,1] => 1000101111 => [1,4,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,2,2,1,1] => 1110101011 => [1,1,1,2,2,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,2,1,1] => 1101101011 => [1,1,2,1,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,2,1,1] => 1011101011 => [1,2,1,1,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,2,2,1,2,1,1] => 1101011011 => [1,1,2,2,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,1,1,2,1,1] => 1001111011 => [1,3,1,1,1,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,2,3,1,1,2] => 1101001110 => [1,1,2,3,1,1,2]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,3,1,2,1,2] => 1100110110 => [1,1,3,1,2,1,2]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,3,2,1,1,2] => 1100101110 => [1,1,3,2,1,1,2]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,1,1,2] => 1100011110 => [1,1,4,1,1,1,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2,1,2] => 1001110110 => [1,3,1,1,2,1,2]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [3,2,1,1,1,2] => 1001011110 => [1,3,2,1,1,1,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,1,1,2] => 1000111110 => [1,4,1,1,1,1,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [2,2,2,2,2,1,1] => 101010101011 => [1,2,2,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [2,2,2,3,1,1,1] => 101010100111 => [1,2,2,2,3,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [2,2,3,1,2,1,1] => 101010011011 => [1,2,2,3,1,2,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [2,2,3,2,1,1,1] => 101010010111 => [1,2,2,3,2,1,1,1]
[1,1,0,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0] => [2,2,4,1,1,1,1] => 101010001111 => [1,2,2,4,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [2,3,1,2,2,1,1] => 101001101011 => [1,2,3,1,2,2,1,1]
[1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [2,3,1,3,1,1,1] => 101001100111 => [1,2,3,1,3,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0] => [2,3,2,1,2,1,1] => 101001011011 => [1,2,3,2,1,2,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1,2,1,1] => 101000111011 => [1,2,4,1,1,2,1,1]
[1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0] => [2,3,2,2,1,1,1] => 101001010111 => [1,2,3,2,2,1,1,1]
[1,1,0,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0] => [2,3,3,1,1,1,1] => 101001001111 => [1,2,3,3,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0] => [2,4,1,2,1,1,1] => 101000110111 => [1,2,4,1,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [2,4,2,1,1,1,1] => 101000101111 => [1,2,4,2,1,1,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,5,1,1,1,1,1] => 101000011111 => [1,2,5,1,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,2,2,1,1] => 100110101011 => [1,3,1,2,2,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [3,1,2,3,1,1,1] => 100110100111 => [1,3,1,2,3,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,3,1,2,1,1] => 100110011011 => [1,3,1,3,1,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,1,3,2,1,1,1] => 100110010111 => [1,3,1,3,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [3,1,4,1,1,1,1] => 100110001111 => [1,3,1,4,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [3,2,1,2,2,1,1] => 100101101011 => [1,3,2,1,2,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [3,2,1,3,1,1,1] => 100101100111 => [1,3,2,1,3,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,1,1,2,2,1,1] => 100011101011 => [1,4,1,1,2,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [3,2,2,1,2,1,1] => 100101011011 => [1,3,2,2,1,2,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0] => [3,3,1,1,2,1,1] => 100100111011 => [1,3,3,1,1,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,1,2,1,1] => 100011011011 => [1,4,1,2,1,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,2,1,1,2,1,1] => 100010111011 => [1,4,2,1,1,2,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0] => [5,1,1,1,2,1,1] => 100001111011 => [1,5,1,1,1,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [3,2,2,2,1,1,1] => 100101010111 => [1,3,2,2,2,1,1,1]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [3,2,3,1,1,1,1] => 100101001111 => [1,3,2,3,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0] => [3,3,1,2,1,1,1] => 100100110111 => [1,3,3,1,2,1,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [3,3,2,1,1,1,1] => 100100101111 => [1,3,3,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [3,4,1,1,1,1,1] => 100100011111 => [1,3,4,1,1,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,2,2,1,1,1] => 100011010111 => [1,4,1,2,2,1,1,1]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,3,1,1,1,1] => 100011001111 => [1,4,1,3,1,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0] => [4,2,1,2,1,1,1] => 100010110111 => [1,4,2,1,2,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,1,2,1,1,1] => 100001110111 => [1,5,1,1,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [4,2,2,1,1,1,1] => 100010101111 => [1,4,2,2,1,1,1,1]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [4,3,1,1,1,1,1] => 100010011111 => [1,4,3,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,1,1,1,1] => 100001101111 => [1,5,1,2,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [5,2,1,1,1,1,1] => 100001011111 => [1,5,2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [6,1,1,1,1,1,1] => 100000111111 => [1,6,1,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,2,2,1,1] => 110101101011 => [1,1,2,2,1,2,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1,1,2,1,1] => 100101111011 => [1,3,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 100111111 => [1,3,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,1,1,2,2] => 1011111010 => [1,2,1,1,1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,1,2] => 100111110 => [1,3,1,1,1,1,2]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1,1] => 1000111111 => [1,4,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1,1] => 1010111111 => [1,2,2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1,1] => 1101011111 => [1,1,2,2,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,2,1,1,1] => 1001010111 => [1,3,2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,2,2,1] => 110101010101 => [1,1,2,2,2,2,2,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [3,3,1,1,1] => 100100111 => [1,3,3,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [3,3,1,1,2] => 1001001110 => [1,3,3,1,1,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [3,2,2,1,1] => 100101011 => [1,3,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,1,2,2] => 110011010 => [1,1,3,1,2,2]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,1,1,3,1] => 1000111001 => [1,4,1,1,3,1]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,1,3,1,1] => 1000110011 => [1,4,1,3,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,1,1,2,1] => 1000111101 => [1,4,1,1,1,2,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,1,4] => 1000111000 => [1,4,1,1,4]
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [9,2] => 10000000010 => [1,9,2]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [11,1] => 100000000001 => [1,11,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,1,1,2] => 1110111110 => [1,1,1,2,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => 110111010 => [1,1,2,1,1,2,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,1,1,2] => 1111011110 => [1,1,1,1,2,1,1,1,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => 110111010 => [1,1,2,1,1,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,2,1,1,2] => 1111101110 => [1,1,1,1,1,2,1,1,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => 110111010 => [1,1,2,1,1,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,2,1,2] => 1111110110 => [1,1,1,1,1,1,2,1,2]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [5,1,1,2,1] => 1000011101 => [1,5,1,1,2,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [3,2,1,2,1] => 100101101 => [1,3,2,1,2,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0] => [7,1,2] => 1000000110 => [1,7,1,2]
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1,1] => 111000111 => [1,1,1,4,1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1,1,1,1,1] => 100000111111 => [1,6,1,1,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1,1,1] => 1000101111 => [1,4,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,4,2,1,1,1] => 1100010111 => [1,1,4,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1,1,1] => 1100001111 => [1,1,5,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,6,1,1,1,1,1] => 110000011111 => [1,1,6,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,5,1,1,1] => 110000111 => [1,1,5,1,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,1,1] => 101100011 => [1,2,1,4,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,1,3,1] => 100111001 => [1,3,1,1,3,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,2,1] => 100110101 => [1,3,1,2,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,3,2,1,1] => 101001011 => [1,2,3,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,1] => 100100011 => [1,3,4,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2,1,2] => 100110110 => [1,3,1,2,1,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1,1] => 1010101111 => [1,2,2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,1,2,2] => 100111010 => [1,3,1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,1,1,2,1,1] => 1001111011 => [1,3,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,1,1,2,1,1] => 1001111011 => [1,3,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,1,1,3,1] => 1001111001 => [1,3,1,1,1,3,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,1,2] => 1001111110 => [1,3,1,1,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1,1] => 1001011111 => [1,3,2,1,1,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1,1] => 1010101111 => [1,2,2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [2,3,3,1,1] => 1010010011 => [1,2,3,3,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [2,4,1,2,1] => 1010001101 => [1,2,4,1,2,1]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,5,1,1,1] => 1010000111 => [1,2,5,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,2,3,1] => 1001101001 => [1,3,1,2,3,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0] => [3,3,1,1,2] => 1001001110 => [1,3,3,1,1,2]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [4,1,2,1,2] => 1000110110 => [1,4,1,2,1,2]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,1,4,1] => 1001110001 => [1,3,1,1,4,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [5,1,1,2,1] => 1000011101 => [1,5,1,1,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0] => [7,1,2] => 1000000110 => [1,7,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,1,1,2] => 1000011110 => [1,5,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1,1,1] => 1001111111 => [1,3,1,1,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => 110011111 => [1,1,3,1,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,3,3,1,1] => 110010011 => [1,1,3,3,1,1]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,3,5,1] => 1100100001 => [1,1,3,5,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,4,1,1] => 110100011 => [1,1,2,4,1,1]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,6,1] => 1101000001 => [1,1,2,6,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,1,2,2,1] => 101110101 => [1,2,1,1,2,2,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,1,3,1] => 101111001 => [1,2,1,1,1,3,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,2,3,2,1] => 110100101 => [1,1,2,3,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,3,1,2] => 110100110 => [1,1,2,3,1,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,1,2,2] => 110111010 => [1,1,2,1,1,2,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [4,2,1,2] => 100010110 => [1,4,2,1,2]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,2,3,2,1,1] => 1101001011 => [1,1,2,3,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2,2] => 1101001010 => [1,1,2,3,2,2]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,2,3,2,1,1] => 1101001011 => [1,1,2,3,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,1,2] => 100011110 => [1,4,1,1,1,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,3,1,2,1] => 1101001101 => [1,1,2,3,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => 101111010 => [1,2,1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,1,1,2] => 10011111110 => [1,3,1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,1,2,2,1] => 101110101 => [1,2,1,1,2,2,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,8,2] => 11000000010 => [1,1,8,2]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,7,1] => 1010000001 => [1,2,7,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,7,1] => 1110000001 => [1,1,1,7,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,3,1,1] => 110110011 => [1,1,2,1,3,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1,1] => 110100111 => [1,1,2,3,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1,1] => 1010001111 => [1,2,4,1,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => 101001111 => [1,2,3,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,2,1,1,2] => 1000101110 => [1,4,2,1,1,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => 100001111 => [1,5,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,4,2,1] => 111000101 => [1,1,1,4,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [2,5,1,1,1] => 1010000111 => [1,2,5,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1,1] => 1010110111 => [1,2,2,1,2,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,2,3,2,1] => 1010100101 => [1,2,2,3,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 1000100111 => [1,4,3,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,2,1,2,1] => 1000101101 => [1,4,2,1,2,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,2,3,1] => 1001101001 => [1,3,1,2,3,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [4,3,1,1,1] => 1000100111 => [1,4,3,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [3,3,2,1,1] => 1001001011 => [1,3,3,2,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,1,1] => 1000011011 => [1,5,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1,2,1] => 1110101101 => [1,1,1,2,2,1,2,1]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,4,3,1] => 1110001001 => [1,1,1,4,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,3,2,3,1] => 1100101001 => [1,1,3,2,3,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,3,4,1,1] => 1100100011 => [1,1,3,4,1,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,4,1,1] => 1001100011 => [1,3,1,4,1,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,2,1,2,2,1,1] => 1101101011 => [1,1,2,1,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => [3,3,2,1,1] => 1001001011 => [1,3,3,2,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,1,1,2,1,1] => 1001111011 => [1,3,1,1,1,2,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,3,3,1,2] => 1100100110 => [1,1,3,3,1,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => [1,5,1,1,2] => 1100001110 => [1,1,5,1,1,2]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,2,2] => 1101001010 => [1,1,2,3,2,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [3,3,1,1,2] => 1001001110 => [1,3,3,1,1,2]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [2,1,2,3,2] => 1011010010 => [1,2,1,2,3,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [5,1,1,1,2] => 1000011110 => [1,5,1,1,1,2]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0] => [2,3,2,1,2] => 1010010110 => [1,2,3,2,1,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0] => [2,3,3,1,1,1,1] => 101001001111 => [1,2,3,3,1,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0] => [2,3,2,1,2,1,1] => 101001011011 => [1,2,3,2,1,2,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0] => [2,5,1,1,1,1,1] => 101000011111 => [1,2,5,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0] => [2,4,1,2,1,1,1] => 101000110111 => [1,2,4,1,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [2,2,1,2,3,1,1] => 101011010011 => [1,2,2,1,2,3,1,1]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [2,2,1,4,1,1,1] => 101011000111 => [1,2,2,1,4,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [2,2,3,2,1,1,1] => 101010010111 => [1,2,2,3,2,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0] => [2,4,1,2,1,1,1] => 101000110111 => [1,2,4,1,2,1,1,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0] => [2,2,3,1,1,2,1] => 101010011101 => [1,2,2,3,1,1,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,2,2,1,2,2,1] => 101010110101 => [1,2,2,2,1,2,2,1]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0] => [2,4,1,1,1,2,1] => 101000111101 => [1,2,4,1,1,1,2,1]
[1,1,0,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [2,3,1,2,1,2,1] => 101001101101 => [1,2,3,1,2,1,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [4,2,1,2,1,1,1] => 100010110111 => [1,4,2,1,2,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,3,1,1,1] => 100011100111 => [1,4,1,1,3,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,1,1,2,1,2,1] => 100011101101 => [1,4,1,1,2,1,2,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [3,1,2,3,1,1,1] => 100110100111 => [1,3,1,2,3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,2,1,2,1] => 100110101101 => [1,3,1,2,2,1,2,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,3,1,1,1,1,1] => 100010011111 => [1,4,3,1,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,2,1,2,1,1,1] => 100010110111 => [1,4,2,1,2,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,1,1,1,1,1,1] => 100000111111 => [1,6,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,1,1,1,1] => 100001101111 => [1,5,1,2,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [3,1,2,3,1,1,1] => 100110100111 => [1,3,1,2,3,1,1,1]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [3,1,4,1,1,1,1] => 100110001111 => [1,3,1,4,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0] => [3,3,2,1,1,1,1] => 100100101111 => [1,3,3,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0] => [5,1,2,1,1,1,1] => 100001101111 => [1,5,1,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1,2,1,1] => 100100111011 => [1,3,3,1,1,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [3,2,1,2,2,1,1] => 100101101011 => [1,3,2,1,2,2,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [5,1,1,1,2,1,1] => 100001111011 => [1,5,1,1,1,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,1,2,1,1] => 100011011011 => [1,4,1,2,1,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,3,1,1,1] => 110010100111 => [1,1,3,2,3,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,2,2,1,2,1] => 110010101101 => [1,1,3,2,2,1,2,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,1,0] => [1,3,4,1,1,1,1] => 110010001111 => [1,1,3,4,1,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,3,1,2,1,1] => 110010011011 => [1,1,3,3,1,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,2,3,1,1,1] => 100110100111 => [1,3,1,2,3,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [3,1,2,2,1,2,1] => 100110101101 => [1,3,1,2,2,1,2,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [3,1,4,1,1,1,1] => 100110001111 => [1,3,1,4,1,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,3,1,2,1,1] => 100110011011 => [1,3,1,3,1,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [3,3,4,1,1] => 100100100011 => [1,3,3,4,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,3,3,1,2,1,1] => 110010011011 => [1,1,3,3,1,2,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1,2,1,1] => 110000111011 => [1,1,5,1,1,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,2,2,1,1] => 110100101011 => [1,1,2,3,2,2,1,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => [1,4,1,2,2,1,1] => 110001101011 => [1,1,4,1,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,3,1,1,2,1,1] => 100100111011 => [1,3,3,1,1,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,2,2,1,1] => 100101101011 => [1,3,2,1,2,2,1,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [3,1,1,3,2,1,1] => 100111001011 => [1,3,1,1,3,2,1,1]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => [2,1,2,3,2,1,1] => 101101001011 => [1,2,1,2,3,2,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0] => [3,3,1,1,2,1,1] => 100100111011 => [1,3,3,1,1,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0] => [5,1,1,1,2,1,1] => 100001111011 => [1,5,1,1,1,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1,1,2,1,1] => 101101111011 => [1,2,1,2,1,1,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [2,3,2,1,2,1,1] => 101001011011 => [1,2,3,2,1,2,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,1,2,1,1] => 100011011011 => [1,4,1,2,1,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1,1] => 101101111 => [1,2,1,2,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,1,3,2,1] => 101100101 => [1,2,1,3,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => 101110100 => [1,2,1,1,2,3]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [2,2,3,2] => 101010010 => [1,2,2,3,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [2,4,1,2] => 101000110 => [1,2,4,1,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,2,3,1,1] => 101010011 => [1,2,2,3,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,1,3] => 101011100 => [1,2,2,1,1,3]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,3,3,1] => 101001001 => [1,2,3,3,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,5,1,1] => 101000011 => [1,2,5,1,1]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,1,4] => 101011000 => [1,2,2,1,4]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,1,1] => 1001100011 => [1,3,1,4,1,1]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,2,3,2] => 1011010010 => [1,2,1,2,3,2]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,1,4,1] => 1001110001 => [1,3,1,1,4,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,2,3,2] => 1011010010 => [1,2,1,2,3,2]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,1,4,1] => 1001110001 => [1,3,1,1,4,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,2,1,4,1] => 1010110001 => [1,2,2,1,4,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,3,1] => 1001101001 => [1,3,1,2,3,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,1,4,1] => 1001110001 => [1,3,1,1,4,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,2,1,3,2] => 1010110010 => [1,2,2,1,3,2]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,1,4,1] => 1001110001 => [1,3,1,1,4,1]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [2,2,1,3,2] => 1010110010 => [1,2,2,1,3,2]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,1,1] => 1001100011 => [1,3,1,4,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,3,2,1] => 1001100101 => [1,3,1,3,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,1,2,1] => 1000011101 => [1,5,1,1,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [2,4,1,2,1] => 1010001101 => [1,2,4,1,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,1,1,2,1] => 1000011101 => [1,5,1,1,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [2,4,1,1,2] => 1010001110 => [1,2,4,1,1,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,1,1,2,1] => 1000011101 => [1,5,1,1,2,1]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [5,1,2,1,1] => 1000011011 => [1,5,1,2,1,1]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,2,1,1] => 1000101011 => [1,4,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,1,1] => 1000011011 => [1,5,1,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1,2,1] => 1000101101 => [1,4,2,1,2,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,1,1] => 1000011011 => [1,5,1,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [3,1,3,1,2] => 1001100110 => [1,3,1,3,1,2]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [4,1,3,1,1] => 1000110011 => [1,4,1,3,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2,2] => 1001101010 => [1,3,1,2,2,2]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2,2] => 1001101010 => [1,3,1,2,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,3,1] => 1000111001 => [1,4,1,1,3,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [3,2,1,3,1] => 1001011001 => [1,3,2,1,3,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,1,2,2,1] => 1000110101 => [1,4,1,2,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [4,1,1,3,1] => 1000111001 => [1,4,1,1,3,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,1,2,2] => 1001011010 => [1,3,2,1,2,2]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,1,3,1] => 1000111001 => [1,4,1,1,3,1]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [3,2,1,2,2] => 1001011010 => [1,3,2,1,2,2]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [4,1,3,1,1] => 1000110011 => [1,4,1,3,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,2,1] => 1000110101 => [1,4,1,2,2,1]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,3,2,2,1,1] => 100100101011 => [1,3,3,2,2,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,3,1,1,4] => 101100111000 => [1,2,1,3,1,1,4]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,1,1,4] => 101100111000 => [1,2,1,3,1,1,4]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,1,2,2,3] => 100111010100 => [1,3,1,1,2,2,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,1,2,2,3] => 100111010100 => [1,3,1,1,2,2,3]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [3,1,2,4,1,1] => 100110100011 => [1,3,1,2,4,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,3,1,1] => 100010110011 => [1,4,2,1,3,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,3,1,2] => 100011100110 => [1,4,1,1,3,1,2]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,3,1,2] => 100011100110 => [1,4,1,1,3,1,2]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [3,3,1,1,2,2] => 100100111010 => [1,3,3,1,1,2,2]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,3,1,1] => 100110011 => [1,3,1,3,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [8,2] => 1000000010 => [1,8,2]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [8,2] => 1000000010 => [1,8,2]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2,2] => 110101010 => [1,1,2,2,2,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1,2,1] => 111101101 => [1,1,1,1,2,1,2,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0] => [11,1] => 100000000001 => [1,11,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => [8,1,1] => 1000000011 => [1,8,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0] => [7,2,1] => 1000000101 => [1,7,2,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => 100001101 => [1,5,1,2,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [7,1,1,1] => 1000000111 => [1,7,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => 100011111 => [1,4,1,1,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,1,1] => 110100011 => [1,1,2,4,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,2,3,1] => 110101001 => [1,1,2,2,3,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,4,1,1,1] => 111000111 => [1,1,1,4,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [2,5,1,1,1] => 1010000111 => [1,2,5,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [2,2,4,1,1] => 1010100011 => [1,2,2,4,1,1]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [2,2,2,3,1] => 1010101001 => [1,2,2,2,3,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => 100011101 => [1,4,1,1,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => 100011011 => [1,4,1,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 100110111 => [1,3,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => 101101010 => [1,2,1,2,2,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => 100011010 => [1,4,1,2,2]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,1,1,2,1,1] => 1001111011 => [1,3,1,1,1,2,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,1,2,1,1] => 110011011 => [1,1,3,1,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => 110010111 => [1,1,3,2,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1,1] => 1001011111 => [1,3,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,2,2,1] => 1111110101 => [1,1,1,1,1,1,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,2,1,2,1] => 111101101 => [1,1,1,1,2,1,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,2,3,1] => 1111101001 => [1,1,1,1,1,2,3,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,1,3,1] => 111011001 => [1,1,1,2,1,3,1]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,2,4,1] => 1111010001 => [1,1,1,1,2,4,1]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,1,4,1] => 110110001 => [1,1,2,1,4,1]
[1,0,1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,2,5,1] => 1110100001 => [1,1,1,2,5,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,7,1] => 11110000001 => [1,1,1,1,7,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,1,1,1,1] => 1000001111 => [1,6,1,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => 101001001 => [1,2,3,3,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,2,3] => 101010100 => [1,2,2,2,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [2,3,2,1,1] => 101001011 => [1,2,3,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,2,4,2] => 1010100010 => [1,2,2,4,2]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,2,2,2] => 100101010 => [1,3,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => 101010101 => [1,2,2,2,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => 1000101010 => [1,4,2,2,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,3,2] => 100110010 => [1,3,1,3,2]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,4,1,2] => 1001000110 => [1,3,4,1,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [3,4,4] => 10010001000 => [1,3,4,4]
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2] => 1000000110 => [1,7,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,1,2,1,1] => 1011111011 => [1,2,1,1,1,1,2,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,1,2,1,1] => 1101111011 => [1,1,2,1,1,1,2,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,2,1,1] => 100111011 => [1,3,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,1,2,1] => 1011111101 => [1,2,1,1,1,1,1,2,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,1,3,1] => 111011001 => [1,1,1,2,1,3,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,2,1] => 110100101 => [1,1,2,3,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,1,2,2,1] => 110110101 => [1,1,2,1,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,2,3,2,1] => 1110100101 => [1,1,1,2,3,2,1]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,3,2,2,1] => 1110010101 => [1,1,1,3,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,2,1,4,1] => 1110110001 => [1,1,1,2,1,4,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,1,3,2,1] => 1101100101 => [1,1,2,1,3,2,1]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,2,2,3,1] => 1110101001 => [1,1,1,2,2,3,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,3,3,1] => 1111001001 => [1,1,1,1,3,3,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,2,3,1] => 1101101001 => [1,1,2,1,2,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,4,2,1] => 1111000101 => [1,1,1,1,4,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,2,3,1] => 1110101001 => [1,1,1,2,2,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,1,3,2,1] => 1011100101 => [1,2,1,1,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,2,3,1] => 1011101001 => [1,2,1,1,2,3,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,2,3,1] => 1011101001 => [1,2,1,1,2,3,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [2,2,1,1,3,1] => 1010111001 => [1,2,2,1,1,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,1,1,3,1] => 1001111001 => [1,3,1,1,1,3,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,2,2,2,2,1] => 1101010101 => [1,1,2,2,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,3,2,2,1] => 1110010101 => [1,1,1,3,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,2,1] => 1100110101 => [1,1,3,1,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,2,1,3,1] => 1101011001 => [1,1,2,2,1,3,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,2,3,1] => 1101101001 => [1,1,2,1,2,3,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,2,1] => 1011010101 => [1,2,1,2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,2,1,3,1] => 1011011001 => [1,2,1,2,1,3,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,1,2,2,1] => 1010110101 => [1,2,2,1,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,1,2,2,1] => 1001110101 => [1,3,1,1,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,3,2,1,2,1] => 1100101101 => [1,1,3,2,1,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,1,4,1,2,1] => 1110001101 => [1,1,1,4,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,1,3,1,2,1] => 1011001101 => [1,2,1,3,1,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,4,1,2,1] => 1110001101 => [1,1,1,4,1,2,1]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,2,3,2,2,1] => 111010010101 => [1,1,1,2,3,2,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,4,1,2,2,1] => 111000110101 => [1,1,1,4,1,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,2,1,2,4,1] => 111011010001 => [1,1,1,2,1,2,4,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,1,2,2,2,3,1] => 111010101001 => [1,1,1,2,2,2,3,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,2,3,3,1] => 111101001001 => [1,1,1,1,2,3,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,2,1,2,3,1] => 110101101001 => [1,1,2,2,1,2,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,4,1,3,1] => 111100011001 => [1,1,1,1,4,1,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,4,1,3,1] => 111100011001 => [1,1,1,1,4,1,3,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,2,2,3,1] => 111010101001 => [1,1,1,2,2,2,3,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,2,2,2,2,2,1] => 110101010101 => [1,1,2,2,2,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,2,3,2,2,1] => 111010010101 => [1,1,1,2,3,2,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,2,3,1,2,2,1] => 110100110101 => [1,1,2,3,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,3,1,2,2,2,1] => 110011010101 => [1,1,3,1,2,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1,2,2,1] => 110010110101 => [1,1,3,2,1,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,1,1,2,2,1] => 110001110101 => [1,1,4,1,1,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,3,2,1,3,1] => 111001011001 => [1,1,1,3,2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,1,2,1,3,1] => 110011011001 => [1,1,3,1,2,1,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,2,1,2,3,1] => 110101101001 => [1,1,2,2,1,2,3,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [2,1,2,2,2,2,1] => 101101010101 => [1,2,1,2,2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,1,2,2,1] => 101100110101 => [1,2,1,3,1,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,2,2,1] => 101011010101 => [1,2,2,1,2,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,2,2,1] => 100111010101 => [1,3,1,1,2,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1,2,2,1] => 101010110101 => [1,2,2,2,1,2,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [2,3,1,1,2,2,1] => 101001110101 => [1,2,3,1,1,2,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,1,2,2,1] => 100110110101 => [1,3,1,2,1,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,1,2,2,1] => 100101110101 => [1,3,2,1,1,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [4,1,1,1,2,2,1] => 100011110101 => [1,4,1,1,1,2,2,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [1,3,2,2,1,2,1] => 110010101101 => [1,1,3,2,2,1,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,2,3,2,2,1] => 111010010101 => [1,1,1,2,3,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,4,1,2,1,2,1] => 110001101101 => [1,1,4,1,2,1,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,2,3,2,2,1] => 111010010101 => [1,1,1,2,3,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,2,1,2,1] => 101100101101 => [1,2,1,3,2,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,3,1,2,1] => 101011001101 => [1,2,2,1,3,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,3,1,2,1] => 100111001101 => [1,3,1,1,3,1,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,4,1,2,2,1] => 111000110101 => [1,1,1,4,1,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,4,1,2,2,1] => 111000110101 => [1,1,1,4,1,2,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1,1] => 111100111 => [1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,3,1,1] => 1111110011 => [1,1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,3,1,1,1] => 1111100111 => [1,1,1,1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1,1,1] => 1111001111 => [1,1,1,1,3,1,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 100110000 => [1,3,1,5]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,1,4] => 100011000 => [1,4,1,4]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [5,1,3] => 100001100 => [1,5,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,1,2,2,1] => 1010110101 => [1,2,2,1,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,1,2,2,1] => 1001110101 => [1,3,1,1,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1,2,2,1] => 101010110101 => [1,2,2,2,1,2,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,1,2,2,1] => 101001110101 => [1,2,3,1,1,2,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,2,1,2,2,1] => 100110110101 => [1,3,1,2,1,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,1,1,2,2,1] => 100101110101 => [1,3,2,1,1,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [4,1,1,1,2,2,1] => 100011110101 => [1,4,1,1,1,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,1,1,1,1,2,1] => 101111111101 => [1,2,1,1,1,1,1,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,1,2] => 1001111110 => [1,3,1,1,1,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,1,2] => 1010111110 => [1,2,2,1,1,1,1,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [4,2,1,1,1] => 100010111 => [1,4,2,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [5,2,1,1,1] => 1000010111 => [1,5,2,1,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [2,3,2,1,1] => 101001011 => [1,2,3,2,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,2,1,1] => 1000101011 => [1,4,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,4,1,2,1] => 110001101 => [1,1,4,1,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,2,1,1] => 101011011 => [1,2,2,1,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [4,2,1,1,1,1] => 1000101111 => [1,4,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,2,3] => 100010100 => [1,4,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,3,3] => 100100100 => [1,3,3,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [5,2,2] => 100001010 => [1,5,2,2]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,5,2] => 101000010 => [1,2,5,2]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1,1] => 110101111 => [1,1,2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1,1,1] => 1101011111 => [1,1,2,2,1,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1,1] => 1010001111 => [1,2,4,1,1,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,5,1,1,1,1,1] => 101000011111 => [1,2,5,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,2,1,1,2,1] => 111011101 => [1,1,1,2,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,1,3,1] => 101111001 => [1,2,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,1,1,2,2] => 1011111010 => [1,2,1,1,1,1,2,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 110111100 => [1,1,2,1,1,1,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 110111100 => [1,1,2,1,1,1,3]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,1,2] => 110001110 => [1,1,4,1,1,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 110111100 => [1,1,2,1,1,1,3]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,1,2,2] => 110011010 => [1,1,3,1,2,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,2,2] => 110011010 => [1,1,3,1,2,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1,1] => 101000111 => [1,2,4,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,1,2,1] => 101011101 => [1,2,2,1,1,2,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1,1] => 101100111 => [1,2,1,3,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,1,1,2] => 1000111110 => [1,4,1,1,1,1,2]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,3,1,1,1,1] => 1001001111 => [1,3,3,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,4,2,1,1] => 110001011 => [1,1,4,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => 110001111 => [1,1,4,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,2,3,1,1] => 1101010011 => [1,1,2,2,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,3,1,2,1] => 1101001101 => [1,1,2,3,1,2,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,2,3,2,1,1] => 1101001011 => [1,1,2,3,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,2,4,1,1,1] => 1101000111 => [1,1,2,4,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,1,2,2,1] => 1100110101 => [1,1,3,1,2,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,3,1,1] => 1100110011 => [1,1,3,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,3,2,1,2,1] => 1100101101 => [1,1,3,2,1,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,4,1,1,2,1] => 1100011101 => [1,1,4,1,1,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,2,1] => 1011010101 => [1,2,1,2,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,2,3,1,1] => 1011010011 => [1,2,1,2,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,1,3,1,2,1] => 1011001101 => [1,2,1,3,1,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [2,2,2,2,1,1] => 1010101011 => [1,2,2,2,2,1,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [2,2,3,1,1,1] => 1010100111 => [1,2,2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,2,1,1] => 1010011011 => [1,2,3,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [2,3,2,1,1,1] => 1010010111 => [1,2,3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,2,1,1] => 1001101011 => [1,3,1,2,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,1,3,1,1,1] => 1001100111 => [1,3,1,3,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,2,1,1] => 1001011011 => [1,3,2,1,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,1,2,1,1] => 1000111011 => [1,4,1,1,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [3,2,2,1,1,1] => 1001010111 => [1,3,2,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [3,3,1,1,1,1] => 1001001111 => [1,3,3,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,2,1,1,1] => 1000110111 => [1,4,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [4,2,1,1,1,1] => 1000101111 => [1,4,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1,1,1] => 1000011111 => [1,5,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,2,2,1] => 110101010101 => [1,1,2,2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,2,2,3,1,1] => 110101010011 => [1,1,2,2,2,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,2,3,1,2,1] => 110101001101 => [1,1,2,2,3,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,2,2,3,2,1,1] => 110101001011 => [1,1,2,2,3,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,2,2,4,1,1,1] => 110101000111 => [1,1,2,2,4,1,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,1,2,2,1] => 110100110101 => [1,1,2,3,1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,3,1,1] => 110100110011 => [1,1,2,3,1,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,2,1,2,1] => 110100101101 => [1,1,2,3,2,1,2,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,2,4,1,1,2,1] => 110100011101 => [1,1,2,4,1,1,2,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,2,3,2,2,1,1] => 110100101011 => [1,1,2,3,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,2,3,3,1,1,1] => 110100100111 => [1,1,2,3,3,1,1,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,2,4,1,2,1,1] => 110100011011 => [1,1,2,4,1,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,2,4,2,1,1,1] => 110100010111 => [1,1,2,4,2,1,1,1]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,2,5,1,1,1,1] => 110100001111 => [1,1,2,5,1,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,1,2,2,2,1] => 110011010101 => [1,1,3,1,2,2,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,2,3,1,1] => 110011010011 => [1,1,3,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,3,1,2,1] => 110011001101 => [1,1,3,1,3,1,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,1,3,2,1,1] => 110011001011 => [1,1,3,1,3,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,3,1,4,1,1,1] => 110011000111 => [1,1,3,1,4,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,1,2,2,1] => 110010110101 => [1,1,3,2,1,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,1,3,1,1] => 110010110011 => [1,1,3,2,1,3,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,4,1,1,2,2,1] => 110001110101 => [1,1,4,1,1,2,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,4,1,1,3,1,1] => 110001110011 => [1,1,4,1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [1,3,2,2,1,2,1] => 110010101101 => [1,1,3,2,2,1,2,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [1,3,3,1,1,2,1] => 110010011101 => [1,1,3,3,1,1,2,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,4,1,2,1,2,1] => 110001101101 => [1,1,4,1,2,1,2,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [1,4,2,1,1,2,1] => 110001011101 => [1,1,4,2,1,1,2,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,5,1,1,1,2,1] => 110000111101 => [1,1,5,1,1,1,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,2,2,1] => 101101010101 => [1,2,1,2,2,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,2,2,3,1,1] => 101101010011 => [1,2,1,2,2,3,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,1,2,3,1,2,1] => 101101001101 => [1,2,1,2,3,1,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,1,2,3,2,1,1] => 101101001011 => [1,2,1,2,3,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,1,2,4,1,1,1] => 101101000111 => [1,2,1,2,4,1,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,1,2,2,1] => 101100110101 => [1,2,1,3,1,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,3,1,1] => 101100110011 => [1,2,1,3,1,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [2,1,3,2,1,2,1] => 101100101101 => [1,2,1,3,2,1,2,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [2,1,4,1,1,2,1] => 101100011101 => [1,2,1,4,1,1,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,1,2,2,2,1] => 101011010101 => [1,2,2,1,2,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,2,1,2,3,1,1] => 101011010011 => [1,2,2,1,2,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,3,1,2,1] => 101011001101 => [1,2,2,1,3,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,1,2,2,2,1] => 100111010101 => [1,3,1,1,2,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,1,2,3,1,1] => 100111010011 => [1,3,1,1,2,3,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,3,1,2,1] => 100111001101 => [1,3,1,1,3,1,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [2,2,2,2,2,1,1] => 101010101011 => [1,2,2,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [2,2,2,3,1,1,1] => 101010100111 => [1,2,2,2,3,1,1,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [2,2,3,1,2,1,1] => 101010011011 => [1,2,2,3,1,2,1,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [2,2,3,2,1,1,1] => 101010010111 => [1,2,2,3,2,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [2,2,4,1,1,1,1] => 101010001111 => [1,2,2,4,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,2,2,1,1] => 101001101011 => [1,2,3,1,2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [2,3,1,3,1,1,1] => 101001100111 => [1,2,3,1,3,1,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [2,3,2,1,2,1,1] => 101001011011 => [1,2,3,2,1,2,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1,2,1,1] => 101000111011 => [1,2,4,1,1,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [2,3,2,2,1,1,1] => 101001010111 => [1,2,3,2,2,1,1,1]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [2,3,3,1,1,1,1] => 101001001111 => [1,2,3,3,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [2,4,1,2,1,1,1] => 101000110111 => [1,2,4,1,2,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [2,4,2,1,1,1,1] => 101000101111 => [1,2,4,2,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [3,1,2,2,2,1,1] => 100110101011 => [1,3,1,2,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [3,1,2,3,1,1,1] => 100110100111 => [1,3,1,2,3,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [3,1,3,1,2,1,1] => 100110011011 => [1,3,1,3,1,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [3,1,3,2,1,1,1] => 100110010111 => [1,3,1,3,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [3,1,4,1,1,1,1] => 100110001111 => [1,3,1,4,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,1,2,2,1,1] => 100101101011 => [1,3,2,1,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,1,3,1,1,1] => 100101100111 => [1,3,2,1,3,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,1,1,2,2,1,1] => 100011101011 => [1,4,1,1,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,3,1,1,1] => 100011100111 => [1,4,1,1,3,1,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0] => [3,2,2,1,2,1,1] => 100101011011 => [1,3,2,2,1,2,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [3,3,1,1,2,1,1] => 100100111011 => [1,3,3,1,1,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,1,2,1,2,1,1] => 100011011011 => [1,4,1,2,1,2,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1,2,1,1] => 100010111011 => [1,4,2,1,1,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [5,1,1,1,2,1,1] => 100001111011 => [1,5,1,1,1,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [3,2,2,2,1,1,1] => 100101010111 => [1,3,2,2,2,1,1,1]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0] => [3,2,3,1,1,1,1] => 100101001111 => [1,3,2,3,1,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [3,3,1,2,1,1,1] => 100100110111 => [1,3,3,1,2,1,1,1]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0] => [3,3,2,1,1,1,1] => 100100101111 => [1,3,3,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0] => [3,4,1,1,1,1,1] => 100100011111 => [1,3,4,1,1,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [4,1,2,2,1,1,1] => 100011010111 => [1,4,1,2,2,1,1,1]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [4,1,3,1,1,1,1] => 100011001111 => [1,4,1,3,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,2,1,2,1,1,1] => 100010110111 => [1,4,2,1,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,1,2,1,1,1] => 100001110111 => [1,5,1,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0] => [4,2,2,1,1,1,1] => 100010101111 => [1,4,2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0] => [4,3,1,1,1,1,1] => 100010011111 => [1,4,3,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,2,1,1,1,1] => 100001101111 => [1,5,1,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0] => [5,2,1,1,1,1,1] => 100001011111 => [1,5,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [6,1,1,1,1,1,1] => 100000111111 => [1,6,1,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,1,1,2] => 1010111110 => [1,2,2,1,1,1,1,2]
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
to binary word
Description
Return the composition as a binary word, treating ones as separators.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
searching the database
Sorry, this map was not found in the database.