Prisoners

Prisoners of a camp plan an escape. The only way out passes through a canyon that is $P$ meters long and $L$ meters wide. The canyon has $N$ guards, each standing at a fixed post. Every guard can see up to 100 meters exactly. To avoid being spotted, the prisoners must sneak through the canyon so that the distance to the nearest guard is always strictly greater than 100 meters, as the figure below shows.

The prisoners, tired of violence, want to clear the way out by removing as few guards as possible. Write a program that finds this minimum number.

You may assume the prisoners can remove any guards, including those that other guards can see.

The first line contains three integers $P$ ($1 \le P \le 50000$), $L$ ($1 \le L \le 50000$), and $N$ ($1 \le N \le 250$). Each of the next $N$ lines contains the integer coordinates $X_i$ and $Y_i$ of one guard ($0 \le X_i \le P$, $0 \le Y_i \le L$). The southwest corner of the canyon is $(0, 0)$, and the northeast corner is $(P, L)$.

The prisoners may enter the canyon at any point $(0, Y_s)$ with $0 \le Y_s \le L$, and exit at any point $(P, Y_v)$ with $0 \le Y_v \le L$. $Y_s$ and $Y_v$ do not have to be integers.

Print one non-negative integer on a single line of the text file, the minimum number of guards that must be removed.