Monic quadratic polynomials $P(x)$ and $Q(x)$ have the property that $P(Q(x))$ has zeros at $x=-24,-22,-18,$ and $-16$, and $Q(P(x))$ has zeros at $x=-65,-63,-57,$ and $-55$. What is the sum of the minimum values of $P(x)$ and $Q(x)$?