OLDP - Old problem

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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


Added by:Ruslan Sennov
Date:2009-11-07
Time limit:0.218s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 NODEJS OBJC PERL6 SQLITE VB.NET