Hard Evidence |
The young reporter Janne is planning to take a photo of a secret government installation. He needs to obtain evidence of the many serious crimes against good sense that are being committed there, so as to create a scandal and possibly win a Pulitzer. Unfortunately, the base is surrounded by a high fence with high voltage wires running around. Janne does not want to risk being electrocuted, so he wants to take a photo from outside the fence. He can bring a tripod as high as the fence to take a photo, so if he wants he can stand right beside the fence and take his picture. The secret installation is a convex polygon. The fence has a form of a circle. Of course Janne wants to make a photo with maximal possible detail level.
Consider taking a photo of the base from some point P
The detail level of the photo depends on the view angle of the base at
the point from which the photo is taken. Therefore he wants to find a
point to maximize this angle.
The first line of the input file contains two integer numbers: n
For each test case, write to the output the maximal view angle a
Input
The input file contains several test cases, each of them as described below.
Output
Sample Input
4 2
-1.0 -1.0
1.0 -1.0
1.0 1.0
-1.0 1.0
Sample Output
1.5707963268