BALTIC-WAY 2006 Problem 2

Suppose that the real numbers $a_{i} \in[-2,17], i=1,2, \ldots, 59$, satisfy $a_{1}+a_{2}+\cdots+a_{59}=0$. Prove that

$$a_{1}^{2}+a_{2}^{2}+\cdots+a_{59}^{2} \leq 2006 .$$