Minimum Fraction Sum

Algebra Level 3

\(4\) 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 \(a + b\)?

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