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.