OMCC 2014 Problem 3

Let $a$ , $b$ , $c$ and $d$ be real numbers such that no two of them are equal,

$$\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}=4$$ and $ac=bd$ . Find the maximum possible value of

$$\frac{a}{c}+\frac{b}{d}+\frac{c}{a}+\frac{d}{b}.$$