Let $m, n \in \mathbb{N}^*$. Find the least $n$ for which there exists $m$, such that the rectangle $(3m + 2) \times (4m + 3)$ can be covered with $\frac{n(n + 1)}{2}$ squares, among which there are $n$ squares of length $1$, $n - 1$ squares of length $2$, ..., and $1$ square of length $n$. For the found value of $n$, provide an example of such a covering.

Let's think step by step and output the final answer within \boxed{}.
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