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.