Consider the following optimization problem in positive integers $n_1, n_2, n_3$.

$$\begin{array}{ll} \text{maximize} & n_1(n_2+n_3)\\ \text{subject to} & n_1+n_2+n_3 = N\end{array}$$

If $n_1, n_2, n_3$ were reals, the solution would be $n_1 = \frac N2$ and $n_2 = n_3$. However, in my problem, $n_1, n_2, n_3$ are positive integers. Please help me solve this quadratic integer optimization problem.