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Let $f(x) = x^3+ax^3+bx+c,g(x)=x^3+bx^2+cx+a$ for integers $a,b,c$ with $c\ne 0$. Suppose the following conditions hold:

$f(1)=0$,

The roots of $g(x)=0$ are square of the roots of $f(x) = 0$.

Find the value of $a^{2013}+b^{2013}+c^{2013}$.

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