Question 4The sum of all positive integers $m$ such that $\frac{13!}{m}$ is a perfect square can be written as $2^a 3^b 5^c 7^d 11^e 13^f,$ where $a,$ $b,$ $c,$ $d,$ $e,$ and $f$ are positive integers. Find $a + b + c + d + e + f.$