HMMT November 2024 H8

For all positive integers $r$ and $s$, let $\operatorname{Top}(r, s)$ denote the top number (i.e., numerator) when $\frac{r}{s}$ is written in simplified form. For instance, $\operatorname{Top}(20,24)=5$. Compute the number of ordered pairs of positive integers $(a, z)$ such that $200 \leq a \leq 300$ and $\operatorname{Top}(a, z)=\operatorname{Top}(z, a-1)$.