MEMO 2009 Problem 1

Find all functions $f: \mathbb{R} \to \mathbb{R}$ , such that $$f(xf(y)) + f(f(x) + f(y)) = yf(x) + f(x + f(y))$$ holds for all $x$ , $y \in \mathbb{R}$ , where $\mathbb{R}$ denotes the set of real numbers.