Identifier
Mp00028: Dyck paths —reverse⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Images
[1,0] => [1,0] => 10 => [1,1]
[1,0,1,0] => [1,0,1,0] => 1010 => [1,1,1,1]
[1,1,0,0] => [1,1,0,0] => 1100 => [2,2]
[1,0,1,0,1,0] => [1,0,1,0,1,0] => 101010 => [1,1,1,1,1,1]
[1,0,1,1,0,0] => [1,1,0,0,1,0] => 110010 => [2,2,1,1]
[1,1,0,0,1,0] => [1,0,1,1,0,0] => 101100 => [1,1,2,2]
[1,1,0,1,0,0] => [1,1,0,1,0,0] => 110100 => [2,1,1,2]
[1,1,1,0,0,0] => [1,1,1,0,0,0] => 111000 => [3,3]
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 10101010 => [1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 11001010 => [2,2,1,1,1,1]
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 10110010 => [1,1,2,2,1,1]
[1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 11010010 => [2,1,1,2,1,1]
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 11100010 => [3,3,1,1]
[1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 10101100 => [1,1,1,1,2,2]
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 11001100 => [2,2,2,2]
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 10110100 => [1,1,2,1,1,2]
[1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0] => 11010100 => [2,1,1,1,1,2]
[1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 11100100 => [3,2,1,2]
[1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 10111000 => [1,1,3,3]
[1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0] => 11011000 => [2,1,2,3]
[1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 11101000 => [3,1,1,3]
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 11110000 => [4,4]
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => [1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1100101010 => [2,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 1011001010 => [1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1101001010 => [2,1,1,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => [3,3,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 1010110010 => [1,1,1,1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 1100110010 => [2,2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 1011010010 => [1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => [2,1,1,1,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => [3,2,1,2,1,1]
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => [1,1,3,3,1,1]
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => [2,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => [3,1,1,3,1,1]
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => [4,4,1,1]
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => [1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => [2,2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => [1,1,2,2,2,2]
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => [2,1,1,2,2,2]
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => [3,3,2,2]
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => [1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => [2,2,2,1,1,2]
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => [1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1101010100 => [2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1110010100 => [3,2,1,1,1,2]
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => [1,1,3,2,1,2]
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 1101100100 => [2,1,2,2,1,2]
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 1110100100 => [3,1,1,2,1,2]
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1111000100 => [4,3,1,2]
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => [1,1,1,1,3,3]
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => [2,2,3,3]
[1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => [1,1,2,1,2,3]
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1101011000 => [2,1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => 1110011000 => [3,2,2,3]
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => [1,1,3,1,1,3]
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1101101000 => [2,1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1110101000 => [3,1,1,1,1,3]
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1111001000 => [4,2,1,3]
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => [1,1,4,4]
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => 1101110000 => [2,1,3,4]
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 1110110000 => [3,1,2,4]
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1111010000 => [4,1,1,4]
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => [5,5]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => [2,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => [1,1,2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => [2,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => [3,3,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => [1,1,1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => [2,2,2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => [1,1,2,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => [2,1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => [3,2,1,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => [1,1,3,3,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => [2,1,2,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => [3,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => [4,4,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => [1,1,1,1,1,1,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => [2,2,1,1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => [1,1,2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => [2,1,1,2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => [3,3,2,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => [1,1,1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => [2,2,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => [1,1,2,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => [2,1,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => [3,2,1,1,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => [1,1,3,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => [2,1,2,2,1,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => [3,1,1,2,1,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => [4,3,1,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => [1,1,1,1,3,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => [2,2,3,3,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => [1,1,2,1,2,3,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => [2,1,1,1,2,3,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => [3,2,2,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => [1,1,3,1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => [2,1,2,1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => [3,1,1,1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => [4,2,1,3,1,1]
>>> Load all 1162 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => [1,1,4,4,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => [2,1,3,4,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => [3,1,2,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => [4,1,1,4,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => [5,5,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => [1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => [2,2,1,1,1,1,2,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => [1,1,2,2,1,1,2,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => [2,1,1,2,1,1,2,2]
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => [3,3,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => [1,1,1,1,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => [2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => [1,1,2,1,1,2,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => [2,1,1,1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => [3,2,1,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => [1,1,3,3,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => [2,1,2,3,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => [3,1,1,3,2,2]
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => [4,4,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => [1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => [2,2,1,1,2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => [1,1,2,2,2,1,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => [2,1,1,2,2,1,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => [3,3,2,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => [1,1,1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => [2,2,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => [1,1,2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => [2,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => [3,2,1,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => [1,1,3,2,1,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => [2,1,2,2,1,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => [3,1,1,2,1,1,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => [4,3,1,1,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => [1,1,1,1,3,2,1,2]
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => [2,2,3,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => [1,1,2,1,2,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => [2,1,1,1,2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => [3,2,2,2,1,2]
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => [1,1,3,1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => [2,1,2,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 111010100100 => [3,1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => [4,2,1,2,1,2]
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => [1,1,4,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => [2,1,3,3,1,2]
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => [3,1,2,3,1,2]
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => [4,1,1,3,1,2]
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => [5,4,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => [1,1,1,1,1,1,3,3]
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => [2,2,1,1,3,3]
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => [1,1,2,2,3,3]
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => [2,1,1,2,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => [3,3,3,3]
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => [1,1,1,1,2,1,2,3]
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => [2,2,2,1,2,3]
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => [1,1,2,1,1,1,2,3]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 110101011000 => [2,1,1,1,1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => [3,2,1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => [1,1,3,2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => [2,1,2,2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => [3,1,1,2,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => [4,3,2,3]
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => [1,1,1,1,3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => [2,2,3,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => [1,1,2,1,2,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => [2,1,1,1,2,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => [3,2,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => [1,1,3,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => [2,1,2,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 111010101000 => [3,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => [4,2,1,1,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => [1,1,4,2,1,3]
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => [2,1,3,2,1,3]
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => [3,1,2,2,1,3]
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => [4,1,1,2,1,3]
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => [5,3,1,3]
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => [1,1,1,1,4,4]
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => [2,2,4,4]
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => [1,1,2,1,3,4]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => [2,1,1,1,3,4]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => [3,2,3,4]
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => [1,1,3,1,2,4]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => [2,1,2,1,2,4]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => [3,1,1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => [4,2,2,4]
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => [1,1,4,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => [2,1,3,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => [3,1,2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => [4,1,1,1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => [5,2,1,4]
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => [1,1,5,5]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => [2,1,4,5]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => [3,1,3,5]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => [4,1,2,5]
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => [5,1,1,5]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => [6,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 11001010101010 => [2,2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 10110010101010 => [1,1,2,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 11010010101010 => [2,1,1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 11100010101010 => [3,3,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 10101100101010 => [1,1,1,1,2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 11001100101010 => [2,2,2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 10110100101010 => [1,1,2,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 11010100101010 => [2,1,1,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 11100100101010 => [3,2,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 10111000101010 => [1,1,3,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 11011000101010 => [2,1,2,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 11101000101010 => [3,1,1,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 11110000101010 => [4,4,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 10101011001010 => [1,1,1,1,1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 11001011001010 => [2,2,1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 10110011001010 => [1,1,2,2,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 11010011001010 => [2,1,1,2,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 11100011001010 => [3,3,2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 10101101001010 => [1,1,1,1,2,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 11001101001010 => [2,2,2,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 10110101001010 => [1,1,2,1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 11010101001010 => [2,1,1,1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 11100101001010 => [3,2,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 10111001001010 => [1,1,3,2,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 11011001001010 => [2,1,2,2,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 11101001001010 => [3,1,1,2,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 11110001001010 => [4,3,1,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 10101110001010 => [1,1,1,1,3,3,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 11001110001010 => [2,2,3,3,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 10110110001010 => [1,1,2,1,2,3,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 11010110001010 => [2,1,1,1,2,3,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 11100110001010 => [3,2,2,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 10111010001010 => [1,1,3,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 11011010001010 => [2,1,2,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 11101010001010 => [3,1,1,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 11110010001010 => [4,2,1,3,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 10111100001010 => [1,1,4,4,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 11011100001010 => [2,1,3,4,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 11101100001010 => [3,1,2,4,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 11110100001010 => [4,1,1,4,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 11111000001010 => [5,5,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 10101010110010 => [1,1,1,1,1,1,1,1,2,2,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 11001010110010 => [2,2,1,1,1,1,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 10110010110010 => [1,1,2,2,1,1,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 11010010110010 => [2,1,1,2,1,1,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 11100010110010 => [3,3,1,1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 10101100110010 => [1,1,1,1,2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 11001100110010 => [2,2,2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 10110100110010 => [1,1,2,1,1,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 11010100110010 => [2,1,1,1,1,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 11100100110010 => [3,2,1,2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 10111000110010 => [1,1,3,3,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 11011000110010 => [2,1,2,3,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 11101000110010 => [3,1,1,3,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 11110000110010 => [4,4,2,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 10101011010010 => [1,1,1,1,1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 11001011010010 => [2,2,1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 10110011010010 => [1,1,2,2,2,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 11010011010010 => [2,1,1,2,2,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 11100011010010 => [3,3,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 10101101010010 => [1,1,1,1,2,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 11001101010010 => [2,2,2,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 10110101010010 => [1,1,2,1,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 11010101010010 => [2,1,1,1,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 11100101010010 => [3,2,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 10111001010010 => [1,1,3,2,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 11011001010010 => [2,1,2,2,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 11101001010010 => [3,1,1,2,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 11110001010010 => [4,3,1,1,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 10101110010010 => [1,1,1,1,3,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 11001110010010 => [2,2,3,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 10110110010010 => [1,1,2,1,2,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 11010110010010 => [2,1,1,1,2,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 11100110010010 => [3,2,2,2,1,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 10111010010010 => [1,1,3,1,1,2,1,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 11011010010010 => [2,1,2,1,1,2,1,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 11101010010010 => [3,1,1,1,1,2,1,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 11110010010010 => [4,2,1,2,1,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 10111100010010 => [1,1,4,3,1,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 11011100010010 => [2,1,3,3,1,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 11101100010010 => [3,1,2,3,1,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11110100010010 => [4,1,1,3,1,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => [5,4,1,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 10101011100010 => [1,1,1,1,1,1,3,3,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11001011100010 => [2,2,1,1,3,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10110011100010 => [1,1,2,2,3,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 11010011100010 => [2,1,1,2,3,3,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 11100011100010 => [3,3,3,3,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 10101101100010 => [1,1,1,1,2,1,2,3,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 11001101100010 => [2,2,2,1,2,3,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 10110101100010 => [1,1,2,1,1,1,2,3,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 11010101100010 => [2,1,1,1,1,1,2,3,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 11100101100010 => [3,2,1,1,2,3,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 10111001100010 => [1,1,3,2,2,3,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 11011001100010 => [2,1,2,2,2,3,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 11101001100010 => [3,1,1,2,2,3,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 11110001100010 => [4,3,2,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 10101110100010 => [1,1,1,1,3,1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 11001110100010 => [2,2,3,1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 10110110100010 => [1,1,2,1,2,1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 11010110100010 => [2,1,1,1,2,1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 11100110100010 => [3,2,2,1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 10111010100010 => [1,1,3,1,1,1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 11011010100010 => [2,1,2,1,1,1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 11101010100010 => [3,1,1,1,1,1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 11110010100010 => [4,2,1,1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 10111100100010 => [1,1,4,2,1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 11011100100010 => [2,1,3,2,1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 11101100100010 => [3,1,2,2,1,3,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => [4,1,1,2,1,3,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => [5,3,1,3,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 10101111000010 => [1,1,1,1,4,4,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11001111000010 => [2,2,4,4,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 10110111000010 => [1,1,2,1,3,4,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 11010111000010 => [2,1,1,1,3,4,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 11100111000010 => [3,2,3,4,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 10111011000010 => [1,1,3,1,2,4,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 11011011000010 => [2,1,2,1,2,4,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 11101011000010 => [3,1,1,1,2,4,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => [4,2,2,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 10111101000010 => [1,1,4,1,1,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 11011101000010 => [2,1,3,1,1,4,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => [3,1,2,1,1,4,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => [4,1,1,1,1,4,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => [5,2,1,4,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10111110000010 => [1,1,5,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => [2,1,4,5,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => [3,1,3,5,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => [4,1,2,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => [5,1,1,5,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => [6,6,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10101010101100 => [1,1,1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 11001010101100 => [2,2,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 10110010101100 => [1,1,2,2,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 11010010101100 => [2,1,1,2,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 11100010101100 => [3,3,1,1,1,1,2,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 10101100101100 => [1,1,1,1,2,2,1,1,2,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11001100101100 => [2,2,2,2,1,1,2,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 10110100101100 => [1,1,2,1,1,2,1,1,2,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 11010100101100 => [2,1,1,1,1,2,1,1,2,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 11100100101100 => [3,2,1,2,1,1,2,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10111000101100 => [1,1,3,3,1,1,2,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 11011000101100 => [2,1,2,3,1,1,2,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 11101000101100 => [3,1,1,3,1,1,2,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 11110000101100 => [4,4,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 10101011001100 => [1,1,1,1,1,1,2,2,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 11001011001100 => [2,2,1,1,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 10110011001100 => [1,1,2,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 11010011001100 => [2,1,1,2,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11100011001100 => [3,3,2,2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 10101101001100 => [1,1,1,1,2,1,1,2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 11001101001100 => [2,2,2,1,1,2,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 10110101001100 => [1,1,2,1,1,1,1,2,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 11010101001100 => [2,1,1,1,1,1,1,2,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 11100101001100 => [3,2,1,1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 10111001001100 => [1,1,3,2,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 11011001001100 => [2,1,2,2,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 11101001001100 => [3,1,1,2,1,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 11110001001100 => [4,3,1,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 10101110001100 => [1,1,1,1,3,3,2,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 11001110001100 => [2,2,3,3,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 10110110001100 => [1,1,2,1,2,3,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 11010110001100 => [2,1,1,1,2,3,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 11100110001100 => [3,2,2,3,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 10111010001100 => [1,1,3,1,1,3,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 11011010001100 => [2,1,2,1,1,3,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 11101010001100 => [3,1,1,1,1,3,2,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 11110010001100 => [4,2,1,3,2,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 10111100001100 => [1,1,4,4,2,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 11011100001100 => [2,1,3,4,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 11101100001100 => [3,1,2,4,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 11110100001100 => [4,1,1,4,2,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => [5,5,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10101010110100 => [1,1,1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 11001010110100 => [2,2,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 10110010110100 => [1,1,2,2,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 11010010110100 => [2,1,1,2,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 11100010110100 => [3,3,1,1,2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 10101100110100 => [1,1,1,1,2,2,2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 11001100110100 => [2,2,2,2,2,1,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 10110100110100 => [1,1,2,1,1,2,2,1,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 11010100110100 => [2,1,1,1,1,2,2,1,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 11100100110100 => [3,2,1,2,2,1,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 10111000110100 => [1,1,3,3,2,1,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 11011000110100 => [2,1,2,3,2,1,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 11101000110100 => [3,1,1,3,2,1,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 11110000110100 => [4,4,2,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 10101011010100 => [1,1,1,1,1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 11001011010100 => [2,2,1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 10110011010100 => [1,1,2,2,2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 11010011010100 => [2,1,1,2,2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 11100011010100 => [3,3,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 10101101010100 => [1,1,1,1,2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 11001101010100 => [2,2,2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 10110101010100 => [1,1,2,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 11010101010100 => [2,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 11100101010100 => [3,2,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 10111001010100 => [1,1,3,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 11011001010100 => [2,1,2,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 11101001010100 => [3,1,1,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 11110001010100 => [4,3,1,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 10101110010100 => [1,1,1,1,3,2,1,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 11001110010100 => [2,2,3,2,1,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 10110110010100 => [1,1,2,1,2,2,1,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 11010110010100 => [2,1,1,1,2,2,1,1,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 11100110010100 => [3,2,2,2,1,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 10111010010100 => [1,1,3,1,1,2,1,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 11011010010100 => [2,1,2,1,1,2,1,1,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 11101010010100 => [3,1,1,1,1,2,1,1,1,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11110010010100 => [4,2,1,2,1,1,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 10111100010100 => [1,1,4,3,1,1,1,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 11011100010100 => [2,1,3,3,1,1,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 11101100010100 => [3,1,2,3,1,1,1,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11110100010100 => [4,1,1,3,1,1,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 11111000010100 => [5,4,1,1,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 10101011100100 => [1,1,1,1,1,1,3,2,1,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 11001011100100 => [2,2,1,1,3,2,1,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 10110011100100 => [1,1,2,2,3,2,1,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 11010011100100 => [2,1,1,2,3,2,1,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 11100011100100 => [3,3,3,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 10101101100100 => [1,1,1,1,2,1,2,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 11001101100100 => [2,2,2,1,2,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 10110101100100 => [1,1,2,1,1,1,2,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 11010101100100 => [2,1,1,1,1,1,2,2,1,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 11100101100100 => [3,2,1,1,2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 10111001100100 => [1,1,3,2,2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 11011001100100 => [2,1,2,2,2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 11101001100100 => [3,1,1,2,2,2,1,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 11110001100100 => [4,3,2,2,1,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 10101110100100 => [1,1,1,1,3,1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 11001110100100 => [2,2,3,1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 10110110100100 => [1,1,2,1,2,1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 11010110100100 => [2,1,1,1,2,1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 11100110100100 => [3,2,2,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 10111010100100 => [1,1,3,1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 11011010100100 => [2,1,2,1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 11101010100100 => [3,1,1,1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11110010100100 => [4,2,1,1,1,2,1,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 10111100100100 => [1,1,4,2,1,2,1,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 11011100100100 => [2,1,3,2,1,2,1,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11101100100100 => [3,1,2,2,1,2,1,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 11110100100100 => [4,1,1,2,1,2,1,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11111000100100 => [5,3,1,2,1,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 10101111000100 => [1,1,1,1,4,3,1,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 11001111000100 => [2,2,4,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 10110111000100 => [1,1,2,1,3,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 11010111000100 => [2,1,1,1,3,3,1,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 11100111000100 => [3,2,3,3,1,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 10111011000100 => [1,1,3,1,2,3,1,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 11011011000100 => [2,1,2,1,2,3,1,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11101011000100 => [3,1,1,1,2,3,1,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 11110011000100 => [4,2,2,3,1,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10111101000100 => [1,1,4,1,1,3,1,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11011101000100 => [2,1,3,1,1,3,1,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 11101101000100 => [3,1,2,1,1,3,1,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 11110101000100 => [4,1,1,1,1,3,1,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11111001000100 => [5,2,1,3,1,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => [1,1,5,4,1,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 11011110000100 => [2,1,4,4,1,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11101110000100 => [3,1,3,4,1,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 11110110000100 => [4,1,2,4,1,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 11111010000100 => [5,1,1,4,1,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 11111100000100 => [6,5,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10101010111000 => [1,1,1,1,1,1,1,1,3,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 11001010111000 => [2,2,1,1,1,1,3,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 10110010111000 => [1,1,2,2,1,1,3,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 11010010111000 => [2,1,1,2,1,1,3,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 11100010111000 => [3,3,1,1,3,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10101100111000 => [1,1,1,1,2,2,3,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 11001100111000 => [2,2,2,2,3,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 10110100111000 => [1,1,2,1,1,2,3,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 11010100111000 => [2,1,1,1,1,2,3,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 11100100111000 => [3,2,1,2,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 10111000111000 => [1,1,3,3,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 11011000111000 => [2,1,2,3,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 11101000111000 => [3,1,1,3,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 11110000111000 => [4,4,3,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 10101011011000 => [1,1,1,1,1,1,2,1,2,3]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 11001011011000 => [2,2,1,1,2,1,2,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 10110011011000 => [1,1,2,2,2,1,2,3]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 11010011011000 => [2,1,1,2,2,1,2,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 11100011011000 => [3,3,2,1,2,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 10101101011000 => [1,1,1,1,2,1,1,1,2,3]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 11001101011000 => [2,2,2,1,1,1,2,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 10110101011000 => [1,1,2,1,1,1,1,1,2,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 11010101011000 => [2,1,1,1,1,1,1,1,2,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 11100101011000 => [3,2,1,1,1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 10111001011000 => [1,1,3,2,1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 11011001011000 => [2,1,2,2,1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 11101001011000 => [3,1,1,2,1,1,2,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 11110001011000 => [4,3,1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 10101110011000 => [1,1,1,1,3,2,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 11001110011000 => [2,2,3,2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 10110110011000 => [1,1,2,1,2,2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 11010110011000 => [2,1,1,1,2,2,2,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 11100110011000 => [3,2,2,2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 10111010011000 => [1,1,3,1,1,2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 11011010011000 => [2,1,2,1,1,2,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 11101010011000 => [3,1,1,1,1,2,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11110010011000 => [4,2,1,2,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 10111100011000 => [1,1,4,3,2,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 11011100011000 => [2,1,3,3,2,3]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11101100011000 => [3,1,2,3,2,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 11110100011000 => [4,1,1,3,2,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 11111000011000 => [5,4,2,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 10101011101000 => [1,1,1,1,1,1,3,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 11001011101000 => [2,2,1,1,3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 10110011101000 => [1,1,2,2,3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 11010011101000 => [2,1,1,2,3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 11100011101000 => [3,3,3,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 10101101101000 => [1,1,1,1,2,1,2,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 10110101101000 => [1,1,2,1,1,1,2,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 11010101101000 => [2,1,1,1,1,1,2,1,1,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 11100101101000 => [3,2,1,1,2,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 10111001101000 => [1,1,3,2,2,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 11011001101000 => [2,1,2,2,2,1,1,3]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 11101001101000 => [3,1,1,2,2,1,1,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11110001101000 => [4,3,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 10101110101000 => [1,1,1,1,3,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 11001110101000 => [2,2,3,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 10110110101000 => [1,1,2,1,2,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 11010110101000 => [2,1,1,1,2,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 11100110101000 => [3,2,2,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 10111010101000 => [1,1,3,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 11011010101000 => [2,1,2,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11101010101000 => [3,1,1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 11110010101000 => [4,2,1,1,1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 10111100101000 => [1,1,4,2,1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11011100101000 => [2,1,3,2,1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 11101100101000 => [3,1,2,2,1,1,1,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 11110100101000 => [4,1,1,2,1,1,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11111000101000 => [5,3,1,1,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 10101111001000 => [1,1,1,1,4,2,1,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 11001111001000 => [2,2,4,2,1,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10110111001000 => [1,1,2,1,3,2,1,3]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 11010111001000 => [2,1,1,1,3,2,1,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11100111001000 => [3,2,3,2,1,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10111011001000 => [1,1,3,1,2,2,1,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11011011001000 => [2,1,2,1,2,2,1,3]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 11101011001000 => [3,1,1,1,2,2,1,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 11110011001000 => [4,2,2,2,1,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => [1,1,4,1,1,2,1,3]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 11011101001000 => [2,1,3,1,1,2,1,3]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 11101101001000 => [3,1,2,1,1,2,1,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 11110101001000 => [4,1,1,1,1,2,1,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11111001001000 => [5,2,1,2,1,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => [1,1,5,3,1,3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11011110001000 => [2,1,4,3,1,3]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 11101110001000 => [3,1,3,3,1,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 11110110001000 => [4,1,2,3,1,3]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11111010001000 => [5,1,1,3,1,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 11111100001000 => [6,4,1,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10101011110000 => [1,1,1,1,1,1,4,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 11001011110000 => [2,2,1,1,4,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 10110011110000 => [1,1,2,2,4,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 11010011110000 => [2,1,1,2,4,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 11100011110000 => [3,3,4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 10101101110000 => [1,1,1,1,2,1,3,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 11001101110000 => [2,2,2,1,3,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 10110101110000 => [1,1,2,1,1,1,3,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 11010101110000 => [2,1,1,1,1,1,3,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 11100101110000 => [3,2,1,1,3,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 10111001110000 => [1,1,3,2,3,4]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 11011001110000 => [2,1,2,2,3,4]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11101001110000 => [3,1,1,2,3,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 11110001110000 => [4,3,3,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 10101110110000 => [1,1,1,1,3,1,2,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 11001110110000 => [2,2,3,1,2,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 10110110110000 => [1,1,2,1,2,1,2,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 11010110110000 => [2,1,1,1,2,1,2,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11100110110000 => [3,2,2,1,2,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10111010110000 => [1,1,3,1,1,1,2,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11011010110000 => [2,1,2,1,1,1,2,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 11101010110000 => [3,1,1,1,1,1,2,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 11110010110000 => [4,2,1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => [1,1,4,2,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 11011100110000 => [2,1,3,2,2,4]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 11101100110000 => [3,1,2,2,2,4]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 11110100110000 => [4,1,1,2,2,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 11111000110000 => [5,3,2,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10101111010000 => [1,1,1,1,4,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 11001111010000 => [2,2,4,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10110111010000 => [1,1,2,1,3,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11010111010000 => [2,1,1,1,3,1,1,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 11100111010000 => [3,2,3,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => [1,1,3,1,2,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 11011011010000 => [2,1,2,1,2,1,1,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 11101011010000 => [3,1,1,1,2,1,1,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 11110011010000 => [4,2,2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => [1,1,4,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 11011101010000 => [2,1,3,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 11101101010000 => [3,1,2,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 11110101010000 => [4,1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 11111001010000 => [5,2,1,1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => [1,1,5,2,1,4]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 11011110010000 => [2,1,4,2,1,4]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 11101110010000 => [3,1,3,2,1,4]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 11110110010000 => [4,1,2,2,1,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11111010010000 => [5,1,1,2,1,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 11111100010000 => [6,3,1,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10101111100000 => [1,1,1,1,5,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => [2,2,5,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => [1,1,2,1,4,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 11010111100000 => [2,1,1,1,4,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 11100111100000 => [3,2,4,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => [1,1,3,1,3,5]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 11011011100000 => [2,1,2,1,3,5]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 11101011100000 => [3,1,1,1,3,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 11110011100000 => [4,2,3,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => [1,1,4,1,2,5]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 11011101100000 => [2,1,3,1,2,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 11101101100000 => [3,1,2,1,2,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 11110101100000 => [4,1,1,1,2,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 11111001100000 => [5,2,2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => [1,1,5,1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 11011110100000 => [2,1,4,1,1,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 11101110100000 => [3,1,3,1,1,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 11110110100000 => [4,1,2,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 11111010100000 => [5,1,1,1,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 11111100100000 => [6,2,1,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => [1,1,6,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 11011111000000 => [2,1,5,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 11101111000000 => [3,1,4,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 11110111000000 => [4,1,3,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 11111011000000 => [5,1,2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 11111101000000 => [6,1,1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 11111110000000 => [7,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1010101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1100101010101010 => [2,2,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1101001010101010 => [2,1,1,2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1110001010101010 => [3,3,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1101010010101010 => [2,1,1,1,1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 1110010010101010 => [3,2,1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1011100010101010 => [1,1,3,3,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1101100010101010 => [2,1,2,3,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 1110100010101010 => [3,1,1,3,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 1111000010101010 => [4,4,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1101010100101010 => [2,1,1,1,1,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 1110010100101010 => [3,2,1,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => 1111000100101010 => [4,3,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1010111000101010 => [1,1,1,1,3,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1100111000101010 => [2,2,3,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1101011000101010 => [2,1,1,1,2,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1011101000101010 => [1,1,3,1,1,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1101101000101010 => [2,1,2,1,1,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 1110101000101010 => [3,1,1,1,1,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => 1111001000101010 => [4,2,1,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1101110000101010 => [2,1,3,4,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 1111100000101010 => [5,5,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1010101011001010 => [1,1,1,1,1,1,1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1100101011001010 => [2,2,1,1,1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1101010101001010 => [2,1,1,1,1,1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 1110010101001010 => [3,2,1,1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 1111000101001010 => [4,3,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 1110101001001010 => [3,1,1,1,1,2,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 1111100001001010 => [5,4,1,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1101010110001010 => [2,1,1,1,1,1,2,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1101011010001010 => [2,1,1,1,2,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1011101010001010 => [1,1,3,1,1,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1101101010001010 => [2,1,2,1,1,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1110101010001010 => [3,1,1,1,1,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => 1111100010001010 => [5,3,1,3,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1101011100001010 => [2,1,1,1,3,4,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1011111000001010 => [1,1,5,5,1,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1111110000001010 => [6,6,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1100101010110010 => [2,2,1,1,1,1,1,1,2,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1010101011010010 => [1,1,1,1,1,1,1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1101010101010010 => [2,1,1,1,1,1,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 1110010101010010 => [3,2,1,1,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 1110100101010010 => [3,1,1,2,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 1111000101010010 => [4,3,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1011101001010010 => [1,1,3,1,1,2,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 1110101001010010 => [3,1,1,1,1,2,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => 1111100001010010 => [5,4,1,1,1,2,1,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 1111110000010010 => [6,5,1,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1010101011100010 => [1,1,1,1,1,1,1,1,3,3,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1101010101100010 => [2,1,1,1,1,1,1,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1101010110100010 => [2,1,1,1,1,1,2,1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1011101010100010 => [1,1,3,1,1,1,1,1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1101101010100010 => [2,1,2,1,1,1,1,1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1110101010100010 => [3,1,1,1,1,1,1,1,1,3,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 1111110000100010 => [6,4,1,3,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1110001111000010 => [3,3,4,4,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1101010111000010 => [2,1,1,1,1,1,3,4,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => [6,3,1,4,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1010111110000010 => [1,1,1,1,5,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1100111110000010 => [2,2,5,5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1101011110000010 => [2,1,1,1,4,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1011111010000010 => [1,1,5,1,1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => [5,1,1,1,1,5,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => [6,2,1,5,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1011111100000010 => [1,1,6,6,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1101111100000010 => [2,1,5,6,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => [4,1,3,6,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => [5,1,2,6,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => [6,1,1,6,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => [7,7,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1010101010101100 => [1,1,1,1,1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1100101010101100 => [2,2,1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1011001010101100 => [1,1,2,2,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1101001010101100 => [2,1,1,2,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1110001010101100 => [3,3,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1010110010101100 => [1,1,1,1,2,2,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1011010010101100 => [1,1,2,1,1,2,1,1,1,1,2,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1010101100101100 => [1,1,1,1,1,1,2,2,1,1,2,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1101010100101100 => [2,1,1,1,1,1,1,2,1,1,2,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => 1110101000101100 => [3,1,1,1,1,3,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1010101011001100 => [1,1,1,1,1,1,1,1,2,2,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1101010101001100 => [2,1,1,1,1,1,1,1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 1110101001001100 => [3,1,1,1,1,2,1,2,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 1110101010001100 => [3,1,1,1,1,1,1,3,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => 1110101100001100 => [3,1,1,1,2,4,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1011110100001100 => [1,1,4,1,1,4,2,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 1111100100001100 => [5,2,1,4,2,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1011111000001100 => [1,1,5,5,2,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1101111000001100 => [2,1,4,5,2,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1110111000001100 => [3,1,3,5,2,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 1111101000001100 => [5,1,1,5,2,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1111110000001100 => [6,6,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1010101010110100 => [1,1,1,1,1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1100101010110100 => [2,2,1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1011001010110100 => [1,1,2,2,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1101001010110100 => [2,1,1,2,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 1110001010110100 => [3,3,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1010110010110100 => [1,1,1,1,2,2,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1011010010110100 => [1,1,2,1,1,2,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1011100010110100 => [1,1,3,3,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 1111000010110100 => [4,4,1,1,2,1,1,2]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 1111100000110100 => [5,5,2,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1010101011010100 => [1,1,1,1,1,1,1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1100101011010100 => [2,2,1,1,1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1010110011010100 => [1,1,1,1,2,2,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1010101101010100 => [1,1,1,1,1,1,2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1100101101010100 => [2,2,1,1,2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1010110101010100 => [1,1,1,1,2,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1100110101010100 => [2,2,2,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1011010101010100 => [1,1,2,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1101010101010100 => [2,1,1,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1110010101010100 => [3,2,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1011100101010100 => [1,1,3,2,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1101100101010100 => [2,1,2,2,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1110100101010100 => [3,1,1,2,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 1111000101010100 => [4,3,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1010111001010100 => [1,1,1,1,3,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1100111001010100 => [2,2,3,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1101011001010100 => [2,1,1,1,2,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 1110011001010100 => [3,2,2,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1011101001010100 => [1,1,3,1,1,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1101101001010100 => [2,1,2,1,1,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1110101001010100 => [3,1,1,1,1,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1011110001010100 => [1,1,4,3,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 1111010001010100 => [4,1,1,3,1,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1010101110010100 => [1,1,1,1,1,1,3,2,1,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1101010110010100 => [2,1,1,1,1,1,2,2,1,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1010111010010100 => [1,1,1,1,3,1,1,2,1,1,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1010111100010100 => [1,1,1,1,4,3,1,1,1,2]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 1111010100010100 => [4,1,1,1,1,3,1,1,1,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1101111000010100 => [2,1,4,4,1,1,1,2]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => 1111110000010100 => [6,5,1,1,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1010101011100100 => [1,1,1,1,1,1,1,1,3,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1101010101100100 => [2,1,1,1,1,1,1,1,2,2,1,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1010101110100100 => [1,1,1,1,1,1,3,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1010111010100100 => [1,1,1,1,3,1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1011101010100100 => [1,1,3,1,1,1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1110101010100100 => [3,1,1,1,1,1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => 1111001010100100 => [4,2,1,1,1,1,1,2,1,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1010101111000100 => [1,1,1,1,1,1,4,3,1,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1011110101000100 => [1,1,4,1,1,1,1,3,1,2]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => 1111010101000100 => [4,1,1,1,1,1,1,3,1,2]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 1111110001000100 => [6,3,1,3,1,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1100111110000100 => [2,2,5,4,1,2]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1111101010000100 => [5,1,1,1,1,4,1,2]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 1111110010000100 => [6,2,1,4,1,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1101111100000100 => [2,1,5,5,1,2]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 1111011100000100 => [4,1,3,5,1,2]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 1111101100000100 => [5,1,2,5,1,2]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1111110100000100 => [6,1,1,5,1,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1111111000000100 => [7,6,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1010101010111000 => [1,1,1,1,1,1,1,1,1,1,3,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1100101010111000 => [2,2,1,1,1,1,1,1,3,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1101010010111000 => [2,1,1,1,1,2,1,1,3,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1101010100111000 => [2,1,1,1,1,1,1,2,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1011101000111000 => [1,1,3,1,1,3,3,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => 1111001000111000 => [4,2,1,3,3,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 1111010000111000 => [4,1,1,4,3,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 1111100000111000 => [5,5,3,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1010101011011000 => [1,1,1,1,1,1,1,1,2,1,2,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1010110101011000 => [1,1,1,1,2,1,1,1,1,1,2,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1011010101011000 => [1,1,2,1,1,1,1,1,1,1,2,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1101010101011000 => [2,1,1,1,1,1,1,1,1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => 1110101010011000 => [3,1,1,1,1,1,1,2,2,3]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1101111000011000 => [2,1,4,4,2,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1010101011101000 => [1,1,1,1,1,1,1,1,3,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 1110001011101000 => [3,3,1,1,3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 1111000011101000 => [4,4,3,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1101010101101000 => [2,1,1,1,1,1,1,1,2,1,1,3]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => 1111100001101000 => [5,4,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1100101110101000 => [2,2,1,1,3,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 1110001110101000 => [3,3,3,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1101010110101000 => [2,1,1,1,1,1,2,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1100111010101000 => [2,2,3,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => 1110011010101000 => [3,2,2,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1011101010101000 => [1,1,3,1,1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1101101010101000 => [2,1,2,1,1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1110101010101000 => [3,1,1,1,1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1111001010101000 => [4,2,1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1011110010101000 => [1,1,4,2,1,1,1,1,1,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1011110100101000 => [1,1,4,1,1,2,1,1,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1011111000101000 => [1,1,5,3,1,1,1,3]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => 1110111000101000 => [3,1,3,3,1,1,1,3]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => 1111100101001000 => [5,2,1,1,1,2,1,3]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 1111110010001000 => [6,2,1,3,1,3]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 1110111100001000 => [3,1,4,4,1,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1111111000001000 => [7,5,1,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1010101011110000 => [1,1,1,1,1,1,1,1,4,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1101001011110000 => [2,1,1,2,1,1,4,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1011010011110000 => [1,1,2,1,1,2,4,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1101010011110000 => [2,1,1,1,1,2,4,4]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 1110010011110000 => [3,2,1,2,4,4]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 1110100011110000 => [3,1,1,3,4,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1111000011110000 => [4,4,4,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1100110101110000 => [2,2,2,1,1,1,3,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1101010101110000 => [2,1,1,1,1,1,1,1,3,4]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 1110001110110000 => [3,3,3,1,2,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1101010110110000 => [2,1,1,1,1,1,2,1,2,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1101101010110000 => [2,1,2,1,1,1,1,1,2,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 1110101010110000 => [3,1,1,1,1,1,1,1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => 1111010100110000 => [4,1,1,1,1,2,2,4]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => 1110111000110000 => [3,1,3,3,2,4]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => 1111101000110000 => [5,1,1,3,2,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1100101111010000 => [2,2,1,1,4,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1101001111010000 => [2,1,1,2,4,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 1110001111010000 => [3,3,4,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1101010111010000 => [2,1,1,1,1,1,3,1,1,4]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => 1111000111010000 => [4,3,3,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1101011011010000 => [2,1,1,1,2,1,2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1010111101010000 => [1,1,1,1,4,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1100111101010000 => [2,2,4,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1101011101010000 => [2,1,1,1,3,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1101101101010000 => [2,1,2,1,2,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => 1111001101010000 => [4,2,2,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1011110101010000 => [1,1,4,1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1101110101010000 => [2,1,3,1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 1110110101010000 => [3,1,2,1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1111010101010000 => [4,1,1,1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 1111100101010000 => [5,2,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1011111001010000 => [1,1,5,2,1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => 1111011001010000 => [4,1,2,2,1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 1111101001010000 => [5,1,1,2,1,1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1010111110010000 => [1,1,1,1,5,2,1,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1011111010010000 => [1,1,5,1,1,2,1,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 1111110010010000 => [6,2,1,2,1,4]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => [1,1,6,3,1,4]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 1111011100010000 => [4,1,3,3,1,4]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1111111000010000 => [7,4,1,4]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1010101111100000 => [1,1,1,1,1,1,5,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1100101111100000 => [2,2,1,1,5,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1101001111100000 => [2,1,1,2,5,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 1110001111100000 => [3,3,5,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1100110111100000 => [2,2,2,1,4,5]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => 1110110101100000 => [3,1,2,1,1,1,2,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 1111010101100000 => [4,1,1,1,1,1,2,5]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => 1111011001100000 => [4,1,2,2,2,5]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => 1111101001100000 => [5,1,1,2,2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1010111110100000 => [1,1,1,1,5,1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1100111110100000 => [2,2,5,1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => 1110011110100000 => [3,2,4,1,1,5]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => 1111001110100000 => [4,2,3,1,1,5]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => 1111100110100000 => [5,2,2,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => [1,1,5,1,1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1101111010100000 => [2,1,4,1,1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 1111101010100000 => [5,1,1,1,1,1,1,5]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1111110010100000 => [6,2,1,1,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => [1,1,6,2,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1101111100100000 => [2,1,5,2,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 1110111100100000 => [3,1,4,2,1,5]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 1111101100100000 => [5,1,2,2,1,5]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1111111000100000 => [7,3,1,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1010111111000000 => [1,1,1,1,6,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1100111111000000 => [2,2,6,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => [1,1,4,1,3,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => [1,1,5,1,2,6]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 1110111011000000 => [3,1,3,1,2,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 1111011011000000 => [4,1,2,1,2,6]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 1111101011000000 => [5,1,1,1,2,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => [1,1,6,1,1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1101111101000000 => [2,1,5,1,1,6]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 1110111101000000 => [3,1,4,1,1,6]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 1111110101000000 => [6,1,1,1,1,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1111111001000000 => [7,2,1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => [1,1,7,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1101111110000000 => [2,1,6,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1110111110000000 => [3,1,5,7]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1111011110000000 => [4,1,4,7]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1111101110000000 => [5,1,3,7]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1111110110000000 => [6,1,2,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1111111010000000 => [7,1,1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1111111100000000 => [8,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => [1,1,8,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => [8,8,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => [1,1,9,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => [1,1,7,1,1,7]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 111111101000000010 => [7,1,1,7,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => [9,9,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => [1,1,10,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 10111111110100000000 => [1,1,8,1,1,8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => [1,1,6,1,2,7]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 101111111001000000 => [1,1,7,2,1,6]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 111111011000000010 => [6,1,2,7,1,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 111111100100000010 => [7,2,1,6,1,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 11111111010000000010 => [8,1,1,8,1,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1111111111000000000010 => [10,10,1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 10111111110010000000 => [1,1,8,2,1,7]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 101111110101000000 => [1,1,6,1,1,1,1,6]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 10111111101010000000 => [1,1,7,1,1,1,1,7]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 101111110010100000 => [1,1,6,2,1,1,1,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 101111101010100000 => [1,1,5,1,1,1,1,1,1,5]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 110011111110000000 => [2,2,7,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 110111111000000010 => [2,1,6,7,1,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 111111100000001100 => [7,7,2,2]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => 111111100000010010 => [7,6,1,2,1,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => 10111111010101000000 => [1,1,6,1,1,1,1,1,1,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 101011111110000000 => [1,1,1,1,7,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 101111111000000010 => [1,1,7,7,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 110011111101000000 => [2,2,6,1,1,6]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 111111010000001100 => [6,1,1,6,2,2]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 111111100000001010 => [7,7,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 11001111111100000000 => [2,2,8,8]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 11111111000000001100 => [8,8,2,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 10111111110000000010 => [1,1,8,8,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 101111100101010000 => [1,1,5,2,1,1,1,1,1,4]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 11111111000000001010 => [8,8,1,1,1,1]
[] => [] => => []
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 110101010101010100 => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 111001010101010100 => [3,2,1,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 110110010101010100 => [2,1,2,2,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 111010010101010100 => [3,1,1,2,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 110101010110010100 => [2,1,1,1,1,1,1,1,2,2,1,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 110101010101100100 => [2,1,1,1,1,1,1,1,1,1,2,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => 110101010110100100 => [2,1,1,1,1,1,1,1,2,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 111010101010100100 => [3,1,1,1,1,1,1,1,1,1,1,2,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 110101010111000100 => [2,1,1,1,1,1,1,1,3,3,1,2]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 111111100100000100 => [7,2,1,5,1,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 110111111000000100 => [2,1,6,6,1,2]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 111111011000000100 => [6,1,2,6,1,2]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 111111101000000100 => [7,1,1,6,1,2]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 111111110000000100 => [8,7,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 110101010101011000 => [2,1,1,1,1,1,1,1,1,1,1,1,2,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 110101010101101000 => [2,1,1,1,1,1,1,1,1,1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 110101010110101000 => [2,1,1,1,1,1,1,1,2,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 110110101010101000 => [2,1,2,1,1,1,1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 111010101010101000 => [3,1,1,1,1,1,1,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 111101010010101000 => [4,1,1,1,1,2,1,1,1,1,1,3]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => 111110010101001000 => [5,2,1,1,1,1,1,2,1,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 111011111000001000 => [3,1,5,5,1,3]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 111111110000001000 => [8,6,1,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 110101010101110000 => [2,1,1,1,1,1,1,1,1,1,3,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 110101010110110000 => [2,1,1,1,1,1,1,1,2,1,2,4]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => 111101010100110000 => [4,1,1,1,1,1,1,2,2,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 110101010111010000 => [2,1,1,1,1,1,1,1,3,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 110101011101010000 => [2,1,1,1,1,1,3,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 110101110101010000 => [2,1,1,1,3,1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => 111100110101010000 => [4,2,2,1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 110111010101010000 => [2,1,3,1,1,1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 111101010101010000 => [4,1,1,1,1,1,1,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => 111110010101010000 => [5,2,1,1,1,1,1,1,1,4]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => 111101111000010000 => [4,1,4,4,1,4]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => 111111110000010000 => [8,5,1,4]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 111011010101100000 => [3,1,2,1,1,1,1,1,2,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 111101010101100000 => [4,1,1,1,1,1,1,1,2,5]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => 111111001010100000 => [6,2,1,1,1,1,1,5]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => 111111100100100000 => [7,2,1,2,1,5]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => 111110111000100000 => [5,1,3,3,1,5]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => 111111110000100000 => [8,4,1,5]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 111110101011000000 => [5,1,1,1,1,1,2,6]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => 111111010011000000 => [6,1,1,2,2,6]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => 111111001101000000 => [6,2,2,1,1,6]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => 111111100101000000 => [7,2,1,1,1,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 110111111001000000 => [2,1,6,2,1,6]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 111111011001000000 => [6,1,2,2,1,6]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => 111111110001000000 => [8,3,1,6]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => 111110110110000000 => [5,1,2,1,2,7]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => 111111010110000000 => [6,1,1,1,2,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 110111111010000000 => [2,1,6,1,1,7]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 111111101010000000 => [7,1,1,1,1,7]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 111111110010000000 => [8,2,1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 110111111100000000 => [2,1,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 111011111100000000 => [3,1,6,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => 111101111100000000 => [4,1,5,8]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => 111110111100000000 => [5,1,4,8]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => 111111011100000000 => [6,1,3,8]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 111111101100000000 => [7,1,2,8]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 111111110100000000 => [8,1,1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 111111111000000000 => [9,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 110010101010101010 => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 110100101010101010 => [2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 110101001010101010 => [2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 110101010010101010 => [2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 110101010100101010 => [2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 110101010101001010 => [2,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 110101010101010010 => [2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10101010101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 11001010101010101010 => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 111000101010101010 => [3,3,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 11010010101010101010 => [2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 110110001010101010 => [2,1,2,3,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 11010100101010101010 => [2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 110101100010101010 => [2,1,1,1,2,3,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 11010101001010101010 => [2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 110101011000101010 => [2,1,1,1,1,1,2,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 11010101010010101010 => [2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 110101010110001010 => [2,1,1,1,1,1,1,1,2,3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 11010101010100101010 => [2,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 110101010101100010 => [2,1,1,1,1,1,1,1,1,1,2,3,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 11010101010101001010 => [2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 11010101010101010010 => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 11010101010101010100 => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1100101010101010101010 => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 11100010101010101010 => [3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 111010001010101010 => [3,1,1,3,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 111100001010101010 => [4,4,1,1,1,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 11010101010101011000 => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1101010101010101010100 => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 111010100010101010 => [3,1,1,1,1,3,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 11110000101010101010 => [4,4,1,1,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 11010101010101110000 => [2,1,1,1,1,1,1,1,1,1,1,1,3,4]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 111010101000101010 => [3,1,1,1,1,1,1,3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 111110000010101010 => [5,5,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11010101010111010000 => [2,1,1,1,1,1,1,1,1,1,3,1,1,4]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 111010101010001010 => [3,1,1,1,1,1,1,1,1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 11111000001010101010 => [5,5,1,1,1,1,1,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 110110101010100010 => [2,1,2,1,1,1,1,1,1,1,1,3,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 11010101011101010000 => [2,1,1,1,1,1,1,1,3,1,1,1,1,4]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 111010101010100010 => [3,1,1,1,1,1,1,1,1,1,1,3,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 111111000000101010 => [6,6,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 11010101110101010000 => [2,1,1,1,1,1,3,1,1,1,1,1,1,4]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 11111100000010101010 => [6,6,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 11010111010101010000 => [2,1,1,1,3,1,1,1,1,1,1,1,1,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 11011010101010101000 => [2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,3]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 11011101010101010000 => [2,1,3,1,1,1,1,1,1,1,1,1,1,4]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 101011001010101010 => [1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 101110001010101010 => [1,1,3,3,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 101010110010101010 => [1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 101100110010101010 => [1,1,2,2,2,2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 110010101010110010 => [2,2,1,1,1,1,1,1,1,1,2,2,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 110011111100000010 => [2,2,6,6,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 101010101010101100 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 110010101010101100 => [2,2,1,1,1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 101100101010101100 => [1,1,2,2,1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 101010101011001100 => [1,1,1,1,1,1,1,1,1,1,2,2,2,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 101111110000001100 => [1,1,6,6,2,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 101010101010111000 => [1,1,1,1,1,1,1,1,1,1,1,1,3,3]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 111111000000111000 => [6,6,3,3]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 111110000011110000 => [5,5,4,4]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 111100001111100000 => [4,4,5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 111000111111000000 => [3,3,6,6]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 10101010101100101010 => [1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 11111110000000101010 => [7,7,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10101010101010101100 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 11001010101010101100 => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,2,2]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 11111110000000111000 => [7,7,3,3]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 11111100000011110000 => [6,6,4,4]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 11111000001111100000 => [5,5,5,5]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 11110000111111000000 => [4,4,6,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 11100011111110000000 => [3,3,7,7]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11111111110000000000 => [10,10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 101010101010110100 => [1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 101010101011010100 => [1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 101010101101010100 => [1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 101010110101010100 => [1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 101011010101010100 => [1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 101101010101010100 => [1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10101010101010110100 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 101010101011100100 => [1,1,1,1,1,1,1,1,1,1,3,2,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 10101010101011010100 => [1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 101010101110010100 => [1,1,1,1,1,1,1,1,3,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 10101010101101010100 => [1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 101010111001010100 => [1,1,1,1,1,1,3,2,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 10101010110101010100 => [1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 101011100101010100 => [1,1,1,1,3,2,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10101011010101010100 => [1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 101110010101010100 => [1,1,3,2,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10101101010101010100 => [1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10110101010101010100 => [1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => 11111100101010100000 => [6,2,1,1,1,1,1,1,1,5]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 11111010101011000000 => [5,1,1,1,1,1,1,1,2,6]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 1111110010101010100000 => [6,2,1,1,1,1,1,1,1,1,1,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 11111001010101010000 => [5,2,1,1,1,1,1,1,1,1,1,4]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 11110101010101100000 => [4,1,1,1,1,1,1,1,1,1,2,5]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1010101010101010101100 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 110100101010101100 => [2,1,1,2,1,1,1,1,1,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 11100101010101010100 => [3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 11111111100100000000 => [9,2,1,8]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => 11111111011000000000 => [8,1,2,9]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 1111111111001000000000 => [10,2,1,9]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => 11111111001010000000 => [8,2,1,1,1,7]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 11111110101100000000 => [7,1,1,1,2,8]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => 1111111110110000000000 => [9,1,2,10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 110100101010110100 => [2,1,1,2,1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 110010101010110100 => [2,2,1,1,1,1,1,1,1,1,2,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 101110101010101000 => [1,1,3,1,1,1,1,1,1,1,1,1,1,3]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 11111111100000000100 => [9,8,1,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 11011111111000000000 => [2,1,8,9]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 11111111101000000000 => [9,1,1,9]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => 11111111100010000000 => [9,3,1,7]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => 11111111100001000000 => [9,4,1,6]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => 11111111100000100000 => [9,5,1,5]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => 11111111100000010000 => [9,6,1,4]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 11111111100000001000 => [9,7,1,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 110011101010101000 => [2,2,3,1,1,1,1,1,1,1,1,3]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 111010101010001100 => [3,1,1,1,1,1,1,1,1,3,2,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 101110101010100100 => [1,1,3,1,1,1,1,1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 11101010101010100100 => [3,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 1111111111010000000000 => [10,1,1,10]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => 111111000000110100 => [6,6,2,1,1,2]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => 111110000011101000 => [5,5,3,1,1,3]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => 111100001111010000 => [4,4,4,1,1,4]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 111000111110100000 => [3,3,5,1,1,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 101101010101011000 => [1,1,2,1,1,1,1,1,1,1,1,1,2,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 111001010101010010 => [3,2,1,1,1,1,1,1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 110011010101010100 => [2,2,2,1,1,1,1,1,1,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 110101010101001100 => [2,1,1,1,1,1,1,1,1,1,1,2,2,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 11110101010101010000 => [4,1,1,1,1,1,1,1,1,1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => 111101000011110000 => [4,1,1,4,4,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 110100111111000000 => [2,1,1,2,6,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 11101111111000000000 => [3,1,7,9]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 111010001111100000 => [3,1,1,3,5,5]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 11110111111000000000 => [4,1,6,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 11111011111000000000 => [5,1,5,9]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => 111110100000111000 => [5,1,1,5,3,3]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => 11111101111000000000 => [6,1,4,9]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => 11111110111000000000 => [7,1,3,9]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 110011011111000000 => [2,2,2,1,5,6]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 111011110000001100 => [3,1,4,6,2,2]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 111000111011100000 => [3,3,3,1,3,5]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => 111101100000111000 => [4,1,2,5,3,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 101101010010101010 => [1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 101011010010101010 => [1,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 10101010101101001010 => [1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 10101010101101010010 => [1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => 110101010010101100 => [2,1,1,1,1,1,1,2,1,1,1,1,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 110011010010101010 => [2,2,2,1,1,2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 11010101100101010100 => [2,1,1,1,1,1,2,2,1,1,1,1,1,1,1,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 10111010101010101000 => [1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,3]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 101111010101010000 => [1,1,4,1,1,1,1,1,1,1,1,4]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 10111110101010100000 => [1,1,5,1,1,1,1,1,1,1,1,5]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 101111001010101000 => [1,1,4,2,1,1,1,1,1,1,1,3]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 10111101010101010000 => [1,1,4,1,1,1,1,1,1,1,1,1,1,4]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 11111111010000000100 => [8,1,1,7,1,2]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 1111111111000000000100 => [10,9,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1010101010101010110100 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 11001010101010110100 => [2,2,1,1,1,1,1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 101100101010110100 => [1,1,2,2,1,1,1,1,1,1,2,1,1,2]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => 111111000001001010 => [6,5,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => 111110000100101010 => [5,4,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => 111100010010101010 => [4,3,1,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 111001001010101010 => [3,2,1,2,1,1,1,1,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 110101010100111000 => [2,1,1,1,1,1,1,1,1,2,3,3]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 110101010011110000 => [2,1,1,1,1,1,1,2,4,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 110101001111010000 => [2,1,1,1,1,2,4,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 110100111101010000 => [2,1,1,2,4,1,1,1,1,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 110011110101010000 => [2,2,4,1,1,1,1,1,1,4]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 101011101010010100 => [1,1,1,1,3,1,1,1,1,2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 101011001011010100 => [1,1,1,1,2,2,1,1,2,1,1,1,1,2]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.