IMO 2017 Problem 2

Let $\mathbb{R}$ be the set of real numbers. Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that, for any real numbers $x$ and $y$ , $$f(f(x)f(y)) + f(x+y) = f(xy).$$

Proposed by Dorlir Ahmeti, Albania