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Ural Regional School Programming Contest 2009

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A. Observation Deck

Time limit: 0.5 second
Memory limit: 64 MB
Would you like to enjoy a bird's-eye panoramic view of Yekaterinburg?
The Antei business, entertainment, and shopping center is situated in the very center of Yekaterinburg. It includes two high-rise buildings, 19- and 50-storey high. Since the new 50-storey building is still under construction, it is not used yet. The older 19-storey building has an observation deck at its rooftop.
Unfortunately, you won't be able to see the whole Yekaterinburg from this observation deck because the huge unfinished new Antei building stands nearby. At first sight, you may think that it blocks the view of a half of the city, but this is not so. Calculate which part of the city is actually blocked by the new Antei building from visitors on the observation deck.
Yekaterinburg has the form of a circle of radius R centered at the point (0, 0). You can assume that the whole city except for the towering Antei buildings is situated in the horizontal plane. Both high-rise Antei buildings have the form of a cylinder. The foundation of the old building is a circle of radius rold meters centered at the point (0, 0) and the foundation of the new building is a circle of radius rnew meters centered at the point (x, y). Both buildings lie entirely inside Yekaterinburg and have no common points. Visitors can walk around the observation deck and watch the city from any point of the deck. A point of the city can't be seen by a visitor if the segment connecting it with the position of the visitor on the observation deck has at least one common point with the new Antei building. A point of the city is blocked from a visitor if it can't be seen from any point on the observation deck.


The first line contains space-separated integers R, rold, and rnew (1 ≤ rold < rnew < R ≤ 1000). The second line contains space-separated integers x and y.


Output the part of the city blocked from a visitor by the 50-storey Antei building as a percentage of the whole city's area precise up to 10−6.


10 1 3
-1 4
Problem Author: Eugene Kurpilyansky
Problem Source: Ural Regional School Programming Contest 2009
To submit the solution for this problem go to the Problem set: 1722. Observation Deck