More fun in 2016, Part 3

Algebra Level 5

Let \(f(x)=x^{2016}\pm x^{2015}\pm \ldots \pm x \pm 1\) be a monic polynomial whose non-leading coefficients are either 1 or \(-1\). If \(f(x)\) has no real roots, what is the maximal number of coefficients \(-1\) the polynomial \(f(x)\) can have?

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