2016's maximum

Algebra Level 3

\[ \large \left( \sum_{\text{cyc}} \dfrac{x^{2016}}{y^{2016} + z^{2016} + 3} \right) + (1-x)(1-y)(1-z) \]

If \(0\leq x,y,z \leq 1 \), find the maximum value of the expression above.

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