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ZOJ Problem Set - 3574
Under Attack II

Time Limit: 5 Seconds      Memory Limit: 65536 KB

Because of the sucessfully calculation in Under Attack I, Doctor is awarded with Courage Cross and promoted to lieutenant. But the war seems to end in never, now Doctor has a new order to help anti-aircraft troops calculate the proper number of supply sites needed for SAMs in battle regions.

According to intel, enemy bombers go straight across battle region and the bombing runs are continous. So their routes divides the region into several parts. The missles SAM needed are provided by supply sites. Because it's dangerous to cross fireline, Ufo suggests that every part of battle regions divided by firelines should have a supply site so that the SAMs can safely get enough ammo.

Now that the task is clear, Doctor is asked to calculate how many supply sites are at least needed. The bombers' routes are lines y=kx+b given in format as k,b, of course k b are same to their ordinary meanings. Assume the battle region is a rectangle with infinity height, the left x-cooridinate and right x-cooridinate are given so that the width of rectangle is fixed.

Input

The input consists of multiple cases.
The first line are the left x-cooridinate a and right x-cooridinate b of battle region. a b are both in the range of [0,1000]. Of course a will not exceed b.
Next lines will describe enemy bombing routes number n.n can be up to 30000.
Following n lines are k and b of each bombing route.k b are in range of [-100000,100000].
It's guaranteed that no three lines (including the two battle region bound lines) will go through one point.

Output

Output the least number of supply sites needed.

Sample Input

1 2
1
1 5

Sample Output

2

Hint

In sample, line y=x+5 divides the region between x=1 and x=2 into two parts, so the outcome is 2.


Author: HE, Qidan
Contest: ZOJ Monthly, February 2012
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