Let G is the convex polygon with area S and perimeter L. We need to know volume of set of points which distance from G is not greater than R.

Input

Number of test cases in first line and three integers S, L and R for each test case. All integers in input are nonnegative and less than 100.

Output

Volume for each test case with 10^-2 precision.

Example

Input:
1
48 57 1

Output:
189.724