angry_birds_again_and_again

Time Limit: 2000 ms Memory Limit: 65536 KiB

Problem Description

The problems called "Angry Birds" and "Angry Birds Again and Again" has been solved by many teams in the series of contest in 2011 Multi-University Training Contest.
 
This time we focus on the yellow bird called Chuck. Chuck can pick up speed and distance when tapped.
 
You can assume that before tapped, Chuck flies along the parabola. When tapped, it changes to fly along the tangent line. The Chuck starts at the coordinates (0, 0). Now you are given the coordinates of the pig (Px, 0), the x-coordinate of the tapping position (Tx) and the initial flying angle of Chuck (α).

∠AOx = α
Please calculate the area surrounded by Chuck’s path and the ground.(The area surrounded by the solid line O-Tapping position-Pig-O)

Input

The first line contains only one integer T (T is about 1000) indicates the number of test cases. For each case there are two integers, px tx, and a float number α.(0 < Tx ≤ Px ≤ 1000, 0 < α <  ) .

Output

One line for each case specifying the distance rounded to three digits.

Sample Input

1
2 1 1.0

Sample Output

0.692

Hint

 

Source

2014年山东省第五届ACM大学生程序设计竞赛