Let $a_1 < a_2 < \cdots < a_k$ denote the sequence of all positive integers between $1$ and $91$ which are relatively prime to $91$, and set $\omega = e^{2\pi i/91}$. Define \[S = \prod_{1\leq q < p\leq k}(\omega^{a_p} - \omega^{a_q}).\] Given that $S$ is a positive integer, compute the number of positive divisors of $S$.

Let's think step by step and output the final answer within \boxed{}.
user