Let f(x)=x³+ax²+bx+c and g(x)=x³+bx²+cx+a, where

a,b,c are integers with c≠0. Suppose that the following conditions hold f(1)=0, the roots of g(x)=0 are the squares of the roots of f(x)=0. Then, find the value of

a²⁰²³+b²⁰²³+c²⁰²³.