Matrices And Determinants

Let $$A=\left[\begin{array}{ccc}2 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 2\end{array}\right]$$. If \(|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} 2 A))|=(16)^{n}\), then \(n\) is equal to :