### 2012 Canadian Computing Competition, Stage 2

## Day 2, Problem 3: The Winds of War

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
`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 co-ordinates (x, y) of the units have y > 0,
- all co-ordinates are integers with absolute value at most 1000000000, and
- the total number
`P`+`T`of units is between 1 and 100

### Input Format

The first line contains `P` and then `T`, separated by spaces.
Subsequently there are `P` lines of the form `x` `y` giving the
enemy units' co-ordinates, and then `T` lines giving the friendly units'
coordinates.

### Output Format

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

### Sample Output

3

Figure 1: Sample input and an optimal net.

All Submissions

Best Solutions

**Point Value:** 30 (partial)

**Time Limit:** 2.00s

**Memory Limit:** 64M

**Added:** Jun 20, 2012

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, TEXT, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

## Comments (Search)

It's quiet in here...