How Many Points of Intersection?

We have two rows. On the top row, there are $a$ points, and on the bottom row, there are $b$ points. Every point on the top row is connected with every point on the bottom row by a segment. The points are arranged so that the number of internal intersection points among the segments is maximized. To achieve this, no three segments should intersect at a single point. The intersection points located on the rows themselves are not counted; any number of segments may intersect at those points. Given $a$ and $b$, compute P(a, b) — the maximum number of intersection points between the two rows. For example, when a = 2 and b = 3, as shown in the figure, P(2, 3) = 3.