Interior Lattice Point

Geometry Level 4

An integer lattice point is a point with coordinates $(n, m)$ , where $n$ and $m$ are integers. As $N$ ranges from 1 to 905, what is the maximum number of integer lattice points in the interior of a triangle with vertices $(0,0),$ $(N, 907-N),$ and $(N+1, 907-N-1)?$

Note: The point $(0,0)$ is not in the interior of any of the triangles described above.