IR-TST 2010 Problem 2

Find all non-decreasing functions $f:\mathbb R^+\cup\{0\}\rightarrow\mathbb R^+\cup\{0\}$ such that for each $x,y\in \mathbb R^+\cup\{0\}$ $$f\left(\frac{x+f(x)}2+y\right)=2x-f(x)+f(f(y)).$$