Let A be a $3 \times 3$ matrix and $\operatorname{det}(A)=2$. If $n=\operatorname{det}(\underbrace{\operatorname{adj}(\operatorname{adj}(\ldots . .(\operatorname{adj} A))}_{2024-\text { times }}))$, then the remainder when $n$ is divided by 9 is equal to __________.