**distinct** integers $p$, $q$, $r$ and $s$ are chosen from the set $\{1,2,3, \ldots, 16, 17\}$. The minimum possible value of $\frac{p}{q}+\frac{r}{s}$ can be written as $\frac{a}{b}$, where $a$ and $b$ are positive, coprime integers. What is the value of $a + b$?