RMO 2013 A2

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 $c\not=0$ . Suppose that the following conditions hold:

[list=a][] $f(1)=0$ , []the roots of $g(x)=0$ are the squares of the roots of $f(x)=0$ .[/list]

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