JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 23

Let $A=\begin{bmatrix}1&a&a\\0&1&b\\0&0&1\end{bmatrix}$, $a,b\in\mathbb R$. If for some $n\in\mathbb N$, $A^n=\begin{bmatrix}1&48&2160\\0&1&96\\0&0&1\end{bmatrix}$ then $n+a+b$ is equal to ______.