Algebraic Diamond- Problem

Algebra Level 5

Find the maximum possible value of

\[\large\ \sum _{ 1\le r<s\le 2016 } { \left( s - r - 1008 \right) {x _ r} {x _ s} }\]

where \(-1\le { x }_{ i } \le 1\) for all \(i = 1,2,3,\ldots,2016\).

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