FKMO 2013 Problem 2

Find all functions $f : \mathbb{R}\to\mathbb{R}$ satisfying following conditions. (a) $f(x) \ge 0$ for all $x \in \mathbb{R}$ . (b) For $a, b, c, d \in \mathbb{R}$ with $ab + bc + cd = 0$ , equality $f(a-b) + f(c-d) = f(a) + f(b+c) + f(d)$ holds.