Score : 600 points
There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).
Let R=10^{10^{10^{10}}}. Ringo performs the following operation:
For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.
Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:
Input is given from Standard Input in the following format:
N x_1 y_1 : x_N y_N
Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.
The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.
2 0 0 1 1
0.5 0.5
If Ringo put Snuke in the region x+y\leq 1, Snuke will fall into the first hole. The probability of this happening is very close to 0.5. Otherwise, Snuke will fall into the second hole, the probability of which happening is also very close to 0.5.
5 0 0 2 8 4 5 2 6 3 10
0.43160120892732328768 0.03480224363653196956 0.13880483535586193855 0.00000000000000000000 0.39479171208028279727