At the vertex of a cone, two men separated from each other. They walked straight on the cone surface getting higher and higher. They headed in different directions. They established their own kingdoms. Now they are looking backward, and thinking about the answer. What's the size of the area, in which the distance from the first man is no more than , and the distance from the second man is no more than ? The distance on a cone means the length of the shortest curve on the cone surface connecting two points.

 The number of test cases.(1<=<=100000)
For each test case:
 The degree of the angle between cone surface and Z-axis.
 The degree of the polar angle of their direction projected on X-Y plane.
 The distance they walked.
 As defined in the description.
All inputs are integers.

For every test case, print the area in one line. 
Answer will be considered correct if the absolute or relative error is no more than .

3
45
135 45
10 8
6 4
2
12 33
0 0
7 9
10
0 180
10 10
5 5

0.623215434549462266033970081480
5.372360120273385497569051949540
54.789408235208057362797262612730

The first example is pictured above. Output the area of green.