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50854 - Area of Triangle Revised

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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Question by Ibrahim Mesecan.

Area of Triangle Revised

Question: You are given the two sides and the inner angle of n-triangles. Find and show the total area and the area of the triangle which has the smallest area.

Input specification
You will be first given a number (n) the number of triangles. Then, in the following n lines you will be given two integers: the two sides of triangle (a and b). Then in the following n lines, you will be given the angle in degrees between the two given sides where 0 ≤ n ≤ 5000, and 0 ≤ angle ≤ 180 and 0 ≤ (a,b) ≤ 500.

Output specification:
Show two floating point numbers with 2 digits precision: total area of the triangles and the area of the triangle with the smallest area.

Sample Input I
5
20 32
13 16
5 51
4 30
4 6
45
20
40
90
30
Sample Output I
409.8 6.0

Explanation: The area of the first triangle (which is also the max area) is 226.274. The area of other triangles are: 35.570, 81.955, 60.0 and 6.0. And, the total area is 409.8.



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