This problem also can't make up its mind

Algebra Level 5

\[ 0 = |x + |x +1 - |x+2 + |x+3 - |x+4 + |x+5 - \cdots - |x+2016|||||| | \]

Find the number of real solutions of \(x \) that satisfy the above equation.

\[\] Notation: \( | \cdot | \) denotes the absolute value function.

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