# More fun in 2016, Part 20

Algebra Level 4

$S=\sum_{1\leq i<j\leq{2016}}x_ix_j$

Find the maximum of $$S$$ if $$\displaystyle \sum_{i=1}^{2016}x_i^2=2$$, where $$x_1,\ldots ,x_{2016}$$ are real numbers.

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