42 - Andrew Stankevich's Contest, Warmup - 1001
The military scientists of Flatland have recently developed the new smart bomb. The main feature of the bomb is that its explosion power can be regulated after the production.
After the bomb was added to the arsenal, the generals have decided to run a series of test xplosions. The equipment department has provided them with three bombs to explode. Since bureaucracy is a significant problem in the modern Flatland, the generals have decided to make all three explosions in one day. They selected the points where the bombs must be placed, and started to choose the destructing power of the bombs to be exploded.
Of course, the generals want to explode as powerful bombs as possible. On the other hand, to analyze the results of the experiment, the craters of the explosions must not intersect. Each crater is a circle, its radius is proportional to the power of the bomb exploded.
Now the generals want to know what is the maximal total power of the bombs they can explode. Help them to find that out! The total power of the bombs is the sum of their powers.
The input file contains multiple test cases. Each test case contains three lines, each contains two integer numbers -- the coordinates of the location where the corresponding bomb must be exploded. Coordinates do not exceed 109 by their absolute value. Points do not belong to the same line.
Output three real numbers for each test case -- for each bomb output the desired radius of the crater after its explosion. The sum of the radii must be maximal possible, but craters must not intersect (although they may touch each other). Your answer must be accurate up to 10-4.
0 0 4 0 4 3
3.000000 1.000000 2.000000