Let $P\left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), Q, R$ and $S$ be four points on the ellipse $9 x^2+4 y^2=36$. Let $P Q$ and $R S$ be mutually perpendicular and pass through the origin. If $\frac{1}{(P Q)^2}+\frac{1}{(R S)^2}=\frac{p}{q}$, where $p$ and $q$ are comprime, then $p+$ q is equal to-