Given that there are $24$ primes between $3$ and $100$, inclusive, what is the number of ordered pairs $(p, a)$ where $p$ is a prime number such that $3 \le p < 100$, and $1 \le a < p$, satisfying the condition $p \mid (a^{p-2} - a)$?

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