Monic quadratic polynomials $P(x)$ and $Q(x)$ have the property that $P(Q(x))$ has zeros at $x=-13,-11,-9,$ and $-7$, and $Q(P(x))$ has zeros at $x=-35,-33,-27,$ and $-25$. What is the sum of the minimum values of $P(x)$ and $Q(x)$?