Let  $w\ne 1$ be a complex cube root of unity. If ${(4+5w+6w^2)}^{n^2+2}+{(6+5w^2+4w)}^{n^2+2}+{(5+6w+4w^2)}^{n^2+2}=0$  and $n\in N$. And  $n\in \left[1,100\right]$  then number of values of  $n$ is