Let | A |=6, where A is a 3 × 3 matrix. If | adj (3 adj ( A^2 · adj (2 A )))|=2^m · 3^n, m, n ∈ N, then m + n is equal to ____.

Let $\displaystyle |\mathrm{A}|=6$, where A is a $\displaystyle 3 \times 3$ matrix. If $\displaystyle \left|\operatorname{adj}\left(3 \operatorname{adj}\left(\mathrm{~A}^2 \cdot \operatorname{adj}(2 \mathrm{~A})\right)\right)\right|=2^{\mathrm{m}} \cdot 3^{\mathrm{n}}, \mathrm{m}, \mathrm{n} \in \mathbf{N}$, then $\displaystyle \mathrm{m}+\mathrm{n}$ is equal to $\displaystyle \_\_\_\_$.