RO-TST 1999 Problem 5

Let $x_1,x_2,\ldots,x_n$ be distinct positive integers. Prove that $$x_1^2+x_2^2 + \cdots + x_n^2 \geq \frac {2n+1}3 ( x_1+x_2+\cdots + x_n).$$ Laurentiu Panaitopol