CMO 1997 Problem 1

Let $x_1,x_2,\ldots ,x_{1997}$ be real numbers satisfying the following conditions: i) $-\dfrac{1}{\sqrt{3}}\le x_i\le \sqrt{3}$ for $i=1,2,\ldots ,1997$ ; ii) $x_1+x_2+\cdots +x_{1997}=-318 \sqrt{3}$ . Determine (with proof) the maximum value of $x^{12}_1+x^{12}_2+\ldots +x^{12}_{1997}$ .