Description

Farmer John has a grass land, which is very large that when you stand in the middle of it, you can not see its edge. Farmer John had built his barn in the center of the grass land, which is rectangle shape of w * h. And now in the barn lives his favourate cow Bessie.

One day, farmer John goes to the market and ties Bessie to one corner of the barn with a rope of length r. Therefore Bessie can wander around the grass land as long as the rope allows her reach that point, meanwhile the rope may not pass through the barn.

Input

The first line contains a number T for the number of test cases. Then T cases follows. For each case there are three real numbers w, h, r (0 < w, h, r <= 1000) on one line.

Output

Output one real number on one line for each test case, the total area of grass land that Bessie can reach. You may assume that grass land is large enough that Bessie will not get out of the grass land. Round and keep three digitals after the decimal point.

Sample Input

4
2 3 2
2 3 3
2 3 5
2 3 6

Sample Output

9.425
21.991
69.115
103.540

Author

cauchy

Source

Sichuan University Programming Contest 2011 Final