Rose windows

Mr. Arnold Gerald Nostik is in charge of designing the main rose window of the new city cathedral. The window is circular, with a diameter of $2r$. Since Mr. A. G. Nostik knows little about virgins, saints, and angels, he is considering a geometric pattern:

Let $n$ be an even integer, at least $4$. Mr. Nostik plans to choose $n$ points, each at a distance $r$ from the center of the window, such that they form the vertices of a regular polygon (the figure below shows an example for n = 8). These points are then joined by straight lines, and the resulting regions are colored as shown in the example (the colors in the example are arbitrary). Note that for n = 8, there are four regions. Number these regions 1, 2, 3, 4, starting from the center of the rose. In general, there are $n/2$ regions.

Help Mr. Nostik determine how much glass of each color is needed to build the window.

Output

For each input triple $r$, $n$, $k$, output on a separate line the area of the $k$-th region of the window, rounded to four decimal digits.