Biggest Slice

You share one large circular pizza with $n-1$ friends. You cut it like this. Rotate the pizza clockwise about its center by the angle $\theta$, then make one straight cut from the center to the right. Repeat the same rotation and the same cut $n$ times in total.

Unless $\theta$ is chosen well, this is not a good way to divide a pizza. Some slices come out larger than others, and when cuts land on top of each other you get fewer than $n$ slices. You do not care about fairness. The largest slice is yours, so you only want its area.

The first line contains the number of test cases $m$. ($1 \le m \le 200$)

Each of the next $m$ lines holds one test case. A line gives the pizza radius $r$ in centimeters, the number of people sharing the pizza $n$, and the rotation angle $\theta$, in that order. $r$ is an integer with $1 \le r \le 100$, and $n$ is an integer with $1 \le n \le 10^8$. $\theta$ is given as three integers, its degrees, its arcminutes, and its arcseconds. The degrees are between $0$ and $359$, the arcminutes and the arcseconds are each between $0$ and $59$, and $\theta$ is greater than $0$.

For each test case, print the area of the largest slice in square centimeters on its own line, rounded to six digits after the decimal point.