Archimedes' circles

Archimedes is remembered for one sentence: "Do not disturb my circles!"

What he was actually working out in the sand is less well known. He drew $N$ black points and $M$ white points.

He was trying to solve this problem. Among the circles determined by three black points, which one holds the most white points inside it? A white point counts as inside when it belongs to the disk that the circle bounds.

Young Andro decided to settle this problem, more than 2000 years old. Andro is confused as usual, so he needs your help. Find the largest number of white points that lie inside a single circle passing through three black points.

The picture shows an example whose answer is $3$. The circle through $A$, $B$ and $C$ holds three white points. The circle through $A$, $B$ and $D$ holds three white points as well. The circle through $B$, $C$ and $D$ holds one white point. No circle passes through $A$, $C$ and $D$.

The first line contains an integer $N$ ($1 \le N \le 200$), the number of black points.

Each of the next $N$ lines contains the coordinates of one black point, two integers whose absolute values are smaller than $10000$.

The next line contains an integer $M$ ($1 \le M \le 200$), the number of white points.

Each of the next $M$ lines contains the coordinates of one white point in the same format.

All points in the input are distinct, and no white point lies on a circle determined by three black points.

Print the largest number of white points inside a single circle determined by three black points. If three black points never determine a circle, print $0$.