The One Polynomial Man

Is it a programming contest? You are given a prime $p$ and two subsets $S$ and $V$ of residues from $0$ to $p-1$. Count the pairs $(a, b)$ that satisfy all three conditions: first, $\left(\prod_{z \in V}\left(\frac{(2a+3b)^2 + 5a^2}{(3a+b)^2} + \frac{(2a+5b)^2 + 3b^2}{(3a+2b)^2} - z\right)\right) \equiv 0$; second, $a \in S$; third, $b \in S$. All operations are performed modulo $p$. When $a \ne b$, the pairs $(a, b)$ and $(b, a)$ count as different. Division by zero is not allowed: if either denominator is zero, the congruence is considered false.

The first line contains a prime $p$ ($2 \le p \le 10^6$). The second line contains $n$, the size of $S$ ($0 \le n \le p$). The third line contains the $n$ distinct elements $S_1, S_2, \dots, S_n$ ($0 \le S_i \le p-1$). The fourth line contains $m$, the size of $V$ ($0 \le m \le p$). The fifth line contains the $m$ distinct elements $V_1, V_2, \dots, V_m$ ($0 \le V_i \le p-1$).

Print one integer: the number of solutions.