RO-NMO 2008 Problem 103

Let $A=\{1,2,\ldots, 2008\}$ . We will say that set $X$ is an $r$ -set if $\emptyset \neq X \subset A$ , and $\sum_{x\in X} x \equiv r \pmod 3$ . Let $X_r$ , $r\in\{0,1,2\}$ be the set of $r$ -sets.

Find which one of $X_r$ has the most elements.