PAMO 2018 Problem 5

Let $a$ , $b$ , $c$ and $d$ be non-zero pairwise different real numbers such that $$\frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} = 4 \text{ and } ac = bd.$$ Show that $$\frac{a}{c} + \frac{b}{d} + \frac{c}{a} + \frac{d}{b} \leq -12$$ and that $-12$ is the maximum.