SMO 2016 Junior Round 2 Question 2

Let $a_1,a_2,\ldots,a_9$ be a sequence of numbers satisfying $0\lt p\le a_i\le q$ for each $i=1,2,\ldots,9$. Prove that $$\frac{a_1}{a_9}+\frac{a_2}{a_8}+\cdots+\frac{a_9}{a_1}\le1+\frac{4(p^2+q^2)}{pq}.$$