Candy with chocolate

Time Limit: 2 Seconds

Memory Limit: 65536 KB

Description

Candy with chocolate Bob likes candies covered with chocolate. One day, Alice gave him a candy without chocolate, it's shaped as a convex regular polyhedron, with n faces, edge length e. Bob wants to cover it with a uniform coat of chocolate. The uniform coat of chocolate is h in thickness. Bob wants to know the volume of the chocolate he needs to do this.

Input

The first line is an integer T(1 ≤ T ≤ 1000), the number of cases.

There are 3 integers n, e, h in one line for each test case. (1 ≤ n, e, h ≤ 100)

Output

For each case, if it there can be a valid convex regular polyhedron corresponding to n, output the volume in a single line, otherwise, output 0. An answer with absolute error no larger than 1e-5 will be accepted. There're T lines in total.

Sample Input

2
1 1 1
6 1 1

Sample Output

0
19.613568

Hint

None

Source

None

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