Canadian Computing Competition: 2012 Stage 2, Day 2, Problem 3

Colonel Trapp is trapped! For several days he has been fighting General Position on a plateau and his mobile command unit is now stuck at $(0,0)$, on the edge of a cliff. But the winds are changing! The Colonel has a secret weapon up his sleeve: the "epsilon net". Your job, as the Colonel's chief optimization officer, is to determine the maximum advantage that a net can yield.

The epsilon net is a device that looks like a parachute, which you can launch to cover any convex shape. (A shape is convex when, for every pair $p,q$ of points it contains, it also contains the entire line segment $\overline{pq}$.) The net shape must include the launch point $(0,0)$.

The General has $P$ enemy units stationed at fixed positions and the Colonel has $T$ friendly units. The advantage of a particular net shape equals the number of enemy units it covers, minus the number of friendly units it covers. The General is not a unit.

You can assume that

• no three points (Trapp's position $(0,0)$, enemy units, and friendly units) lie on a line,
• every two points have distinct $x$-coordinates and $y$-coordinates,
• all coordinates $(x,y)$ of the units have $y>0$,
• all coordinates are integers with absolute value at most $1000000000$, and
• the total number $P+T$ of units is between $1$ and $100$.

Input Specification

The first line contains $P$ and then $T$, separated by spaces. Subsequently, there are $P$ lines of the form $xy$ giving the enemy units' coordinates, and then $T$ lines giving the friendly units' coordinates.

Output Specification

Output a single line with the maximum possible advantage.

Sample Input

5 3
-8 4
-7 11
4 10
10 5
8 2
-5 7
-4 3
5 6

Output for Sample Input

3