Mr. Toto loves spinning different kinds of spinners. He enjoys watching them go round and round, bringing him happiness. While passing beside a shop, suddenly he saw a unique spinner named spinning spinners. The spinner is a fusion of 3 spinners.

First spinner which carries two more spinners in its both ends is X cm long. Interestingly, its wheel is not in the middle, it's located d cm away from the left side. The second spinner is a rectangular shaped spinner which is h cm long and w cm width which is located in the left end of the first spinner. The last spinner which is located on the right side of the first spinner is Equilateral triangular shaped with side a. Both the wheels of second and third spinners are in their centroid.

As it is too amazing to watch some spinners like that, Mr. Toto wonders how much area is covered by the unique spinner  while spinning. As he is not good at mathematics, he wants your help to find out the area.

Note that pi = 3.1416
 

The first line of input contains an integer T, Number of test cases. Each test case contains 3 lines.
First line contains 2 integers x,d . The next line contains 2 integers h,w length and width of the rectangle.And the final line contains one of the triangle a.

T(1<=T<=\(10^5\))
x,d (1<=x,d<=\(10^5 \))
h,w(1<=h,w<=\(10^5 \))
a(1<=a<=\(10^5 \))

For each test case, print the case number and the area that is covered by the spinner with 4 digits after the decimal point.

Input copy	Output copy
3 5 2 2 3 3 6 3 2 3 3 6 3 3 3 3	Case 1: 70.3477 Case 2: 72.4662 Case 3: 82.3976