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Let \(f(n)\) be a function defined on the non-negative integers given the following facts:

  • \(f(0)=f(1)=0 \).

  • \( f(2)=1 \)

  • For \(n>2\), \(f(n)\) gives the smallest positive integer, which does not divide \(n\).

Let \(g(n)=f(f(f(n))) \), find \(g(1)+g(2)+g(3)+\cdots+g(2016) \).

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