Minimum Fraction Sum

Algebra Level 3

44 distinct integers pp, qq, rr and ss are chosen from the set {1,2,3,,16,17}\{1,2,3, \ldots, 16, 17\}. The minimum possible value of pq+rs\frac{p}{q}+\frac{r}{s} can be written as ab\frac{a}{b}, where aa and bb are positive, coprime integers. What is the value of a+ba + b?

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