Why Did the Cow Cross the Road 6

The reason the cow crossed the road is simply that there are so many roads. John's farm has so many roads that a cow can hardly move around without crossing one.

John's farm was recently reorganized. It is now an $N \times N$ grid of small square pastures ($2 \le N \le 100$). A cow can usually walk freely between two adjacent pastures, but some adjacent pairs are separated by a road that the cow must cross to go between them. A tall fence surrounds the farm, so no cow ever leaves it.

There are $K$ cows on John's farm ($1 \le K \le 100$, $K \le N^2$), each in a different pasture. Some pairs of cows cannot meet unless one of them crosses a road. Count how many such pairs there are.

The first line contains $N$, $K$, and $R$.

Each of the next $R$ lines describes one road. A road joins two pastures that are adjacent vertically or horizontally, and it is given as $r$ $c$ $r'$ $c'$ (row, column, row, column). Every number is between $1$ and $N$, inclusive.

Each of the next $K$ lines gives the position of one cow as a row and a column.

Print the number of pairs of cows that cannot meet without crossing a road.