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Updog is watching a plane object with a telescope. The field of vision in the telescope can be described as a circle. The center is at the origin and the radius is R. The object can be seen as a simple polygon of N vertexes. Updog wants to know the area of the part of the object that can be seen in the telescope.
The input will contain several test cases. For each case:
For each test case, output one real number on a separate line, which is the area of the part that can be seen. The result should be rounded to two decimal places.
10 3 0 20 10 0 -10 0
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