SP8816 MRAVOGRA - Mravograd

The hard working ants have built a town called Ant Town. They modeled their town after Manhattan, with H horizontal and V vertical streets which cross in V×O intersections. As ants don't like water, with the first raindrops comes chaos in Ant Town. Town authorities have placed umbrellas under which any number of ants can hide, but only on N intersections. When the rain starts, each ant on an intersection starts running, **using streets**, to the nearest intersection with an umbrella. But, if an ant can choose from more than one such intersection, it panics and, not knowing where to go, **stays on its starting intersection** and gets wet. Town authorities use the name "wet intersections" for such starting intersections. For example, if Ant Town has 10 horizontal and 10 vertical streets, and if there are 4 intersections with umbrellas, then the question marks in the figure represent "wet intersections":   _Picture represents first example. We count streets from left to right from 1 to V and from down upwards from 1 to H._ Write a program which, given the locations of intersections with umbrellas, determines the **number of "wet intersections**" in Ant Town.

The first line contains two integers H and V (1 Horizontal streets are numbered 1 to H, vertical streets 1 to V. The second line contains an integer N (1 Each of the following N lines contains two integer h and v, meaning that there is an umbrella on the crossing of horizontal street h and vertical street v. The locations of all umbrellas will be distinct.

Output the number of "wet intersections" in Ant Town.