Let S ={ m ∈ Z: A^m^2 + A^m =3 I - A^-6}, where A = [2, -1; 1, 0]. Then n ( S ) is equal to ____.

Let $\displaystyle \mathrm{S}=\left\{\mathrm{m} \in \mathbf{Z}: \mathrm{A}^{\mathrm{m}^2}+\mathrm{A}^{\mathrm{m}}=3 \mathrm{I}-\mathrm{A}^{-6}\right\}$, where $\displaystyle \mathrm{A}=\left[\begin{array}{cc}2 & -1 \\ 1 & 0\end{array}\right]$. Then $\displaystyle \mathrm{n}(\mathrm{S})$ is equal to $\displaystyle \_\_\_\_$.