2016 IMO Shortlist A2

Find the smallest real constant $C$ such that for any positive real numbers $a_{1}, a_{2}, a_{3}, a_{4}$ and $a_{5}$ (not necessarily distinct), one can always choose distinct subscripts $i, j, k$ and $l$ such that $$\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{l}}\right| \leq C$$

找到最小的实常数$C$，使得对于任何正实数$a_{1}、a_{2}、a_{3}、a_{4}$和$a_{5}$(不一定不同)，人们总是可以选择不同的下标$i、j、k$和$l$，使得$$\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{l}}\right| \leq C$$