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.


Inspiration.

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