Let \(f(x) = x^3 + ax^2 + bx + c\) and \(g(x) = x^3 + bx^2 + cx + a\), where \(a, b, c\) are integers with \(c \ne 0\).

Suppose that the following conditions hold:

\(f(1) = 0\)

the roots of \(g(x)\) are squares of the roots of \(f(x)\).

Find the value of \(S=a^{2016}+b^{2016}+ c^{2016}\).

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