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Open Ural FU Championship 2013

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C. Nectar Gathering

Time limit: 0.5 second
Memory limit: 64 MB
To make 1 kilogram of honey a bee should make 150000 flights, cover 300000 kilometers and visit 10 million flowers.
There is a beehive at point (0; 0; 0). Not far from the hive there is a grassland with flowers that should be considered as a triangle with vertices (x1; y1; z1), (x2; y2; z2), and (x3; y3; z3). A bee can fly to any point at distance no more than 100 meters from the hive. Find the area of the grassland part, from which bees can gather nectar.


The first line contains coordinates x1, y1, z1. The second line contains coordinates x2, y2, z2. The third line contains coordinates x3, y3, z3. All the coordinates are integers and do not exceed 200 in their absolute values. It is guaranteed that all three vertices of triangle are not on the same line.


Output the required area with an absolute or relative error no more than 10−2.


0 0 0
0 2 0
2 0 0
Problem Author: Mikhail Rubinchik
Problem Source: Open Ural FU Championship 2013
To submit the solution for this problem go to the Problem set: 1983. Nectar Gathering