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USU Championship 2005

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C. Autumn Tide

Time limit: 0.5 second
Memory limit: 64 MB
This summer the covering of the Dynamo stadium pitch was replaced with a new one. For some time it will be necessary to treat it cautiously: the soil mustn't be too moist or too dry. So it is decided to control strictly the amount of watering of the covering. In particular, it's important to know how many millimeters of precipitations fall on the covering every minute during a rain. If this value is not enough, then the covering will be watered additionally. If the value is too large, then the covering should not be watered for some time after the rain. You'll have to calculate this important value.
It would be very easy if there were no people with umbrellas walking on the pitch!
In a short time (in 5 hours) you must work out the first test version of the algorithm. Fortunately, the test version mustn't take into account all of the details. For example, you may neglect the motion of people with umbrellas. Here is the list of the assumptions that your program should take into account:
  • Exactly 1 mm of precipitations fall down on the pitch each minute.
  • All the people in the stadium area hold opened umbrellas.
  • Each umbrella is an upper hemisphere of radius 1 meter.
  • There is no wind, i.e., raindrops fall vertically down until they encounter an obstacle.
  • All the water that has fallen on an umbrella streams down along the shortest way on the hemisphere.
  • The stadium pitch is a completely covered rectangular.
  • Umbrellas do not overlap.
  • There are four high posts in the corners of the pitch (team banners hang there during a match).
  • People in the stadium area are motionless. Their coordinates are known.


The first line contains two integers W and L (1 ≤ W, L ≤ 10000), which are the stadium's dimensions in meters. The third line contains an integer N (1 ≤ N ≤ 1000), which is the number of people in the stadium area. The next N lines contain coordinates of these people in the form X Y (–10000 ≤ X, Y ≤ 10000). The corners of the pitch have coordinates (0, 0), (0, W), (L, 0) and (L, W).


You should output the average amount of precipitations (in millimeters) falling on the pitch in a minute. This number should be given with accuracy to 3 decimal places.


10 10
0.5 2
2 10.1
Problem Author: Pavel Egorov
Problem Source: The Ural State University Championship, October 29, 2005
To submit the solution for this problem go to the Problem set: 1412. Autumn Tide