Let $PQR$ be an acute triangle with circumcenter $O$. $M$ and $N$ points are on $PR$ and $PQ$ respectively so that $QM\perp PR$ and $RN\perp PQ$. Now $\angle MON - \angle P = 90^\circ$ and $\angle POQ - \angle Q = 30^\circ$. If the maximum possible measure of $\angle R$ is $\frac{u}{v}.180^\circ$ for some positive integers $u$ and $v$ with $u<v$ and $gcd(u,v)=1$, compute $u+v$.