International Mathematical Olympiads!

Denote by $\mathbb {R^+}$ the set of all positive real numbers. Let a function $f : \mathbb {R^+} \to \mathbb {R^+}$ be such that

$\large xf\left( { x }^{ 2 } \right) f\left( f\left( y \right) \right) + f\left( yf\left( x \right) \right) = f( xy)\left( f\left( f\left( { x }^{ 2 } \right) \right) + f\left( f\left( { y }^{ 2 } \right) \right) \right)$

for all $x, y \in \mathbb {R^+}$ .

Find $f(2018)$ .