UVa 10432

Summary

Calculate the area of a polygon having equal sides inside a circle.

Explanation

The length of each side of the polygon are same. So if we add the n vertex of the polygon to the center of the circle, then we get n triangles all having same area. Now the angle created at center by any triangle is exactly ${\displaystyle (2\pi /n)}$ and the length of both arms of triangle is r. So the area of any triangle is ${\displaystyle A={\frac {r^{2}\sin({\frac {2\pi }{n}})}{2}}}$. So, area of polygon is ${\displaystyle nA}$.

Notes

2 * acos (0)

(in C / C++) to calculate the value of pi. Otherwise precision error may occur.

Input

2 2000
10 3000
5 100


Output

12.566
314.159
78.488