My brother Imtiaz is little afraid of Geometry. Is it too hard!! Can you help him to understand how easy geometry is!!

Consider the following picture of ABC triangle with “a” side, “b” base and “y” angle.

Now you have to help me to find the area of the given triangle. Note that the valid angle for the given triangle is 0 < y < 180.

In this picture there is angle we can call it "y" angle.

Input

First line of input will contain test case T (1 <= T <= 1000). Each of the next T line contains 3 integers a, b, y (1 <= a, b <= 1000), here a is the side of the triangle, b is base and y is angle.

Output

For each case test you have to print the area of the triangle, if the angle of the triangle is not valid then print “not a valid angle” (without quotes).

Example

Input:
3
12 3 45
2 1 181
2 1 23

Output:
Case 1: 12.727922
Case 2: not a valid angle
Case 3: 0.390731

Problem Setter : Shariful Islam Shaon