Ninhydrin is a test for amino acids. Egg albumin, which contains proteins (polymers of amino acids), gives a positive test with ninhydrin due to the reaction with amino groups.
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.