Given an $n \times n$ matrix $A$ whose $(i,j)$ entry is
$$a_{ij} = \begin{cases} n-j+i & \text{if } j \geq i\\ 0 & \text{otherwise}\end{cases}$$
find its Jordan form.
I know that all the Jordan blocks will have $\lambda = n$ as eigenvalue, but how can I find the size of each block?