AUSTRIAN-POLISH 1994 Problem 1

A function $f: R \to R$ satisfies the conditions: $f (x + 19) \le f (x) + 19$ and $f (x + 94) \ge f (x) + 94$ for all $x \in R$ . Prove that $f (x + 1) = f (x) + 1$ for all $x \in R$ .