1024: SYH’s Easy Probability Problem

Memory Limit：256 MB Time Limit：1.000 S
Judge Style：Text Compare Creator：
Submit：7 Solved：2

Description

There is an xOy-Coordinate system. Horizontal ordinate of point P forms the equidistribution in the range of [-a,a]. Longitudinal ordinate of point P forms the equidistribution in the range of [-b,b]. Now, point P and the original point O forms a rectangle. SYH will give you an area S, could you please tell him the probability which is the area of your rectangle is no smaller than S?

Input

The first line conatins an integer T, means the number of test cases. For each test case, the first line contains three real numbers a, b and S.

Output

For each test case ouput “Case: #x:y” in a single line. x is the test case number (starting from 1), and y is your answer which has been reserved six decimal.

Sample Input Copy 

2

10 5 20

1 1 1

Sample Output Copy 

Case #1: 0.233484
Case #2: 0.000000

HINT

For the second sample, there’s only four points P(1,1), P(1,-1), P(-1,-1), P(-1,1) satisfies SYH’s requirement. But there are infinite points in the range of [-a,a] in X-axis and [-b,b] in Y-axis. so .



1 ≤ T ≤ 102, 0 ≤ |a|, |b| ≤ 104, 0 ≤ S ≤ 108.