ÖMO 1991 Problem 2

Find all functions $f: \mathbb{Z} - \{ 0 \} \rightarrow \mathbb{Q}$ satisfying:

$f \left( \frac{x+y}{3} \right)=\frac {f(x)+f(y)}{2},$ whenever $x,y,\frac{x+y}{3} \in \mathbb{Z} - \{ 0 \}.$