Let $f(x)=x^3+a{x}^2+bx+c$, where $1<a<b<c$. Let $g(x)$ be a polynomial with leading coefficient 1 whose three roots are the reciprocals of the three roots of $f(x)$. What is the coefficient of $x^2$ in $g(x)$ in terms of $a,b,c$?