Peter and Snow Blower

##### **点到多边形的最短距离** 给出一个定点和一个n个点的多边形. 现在将这个多边形绕着定点旋转一圈.问这一圈的面积为多少?多边形绕定点旋转 相等于多变形内所有的点绕定点旋转一圈.为定点到多边形顶点的最远距离,mn为定点到多边形的边的最短距离mn利用向量积来求,注意定点到边的垂足是否在边的延长线上.

Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path. Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine. Peter decided to tie his car to point $ P $ and now he is wondering what is the area of ​​the region that will be cleared from snow. Help him.

The first line of the input contains three integers — the number of vertices of the polygon $ n $ (), and coordinates of point $ P $ . Each of the next $ n $ lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line. All the numbers in the input are integers that do not exceed $ 1000000 $ in their absolute value.

Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed $ 10^{-6} $ . Namely: let's assume that your answer is $ a $ , and the answer of the jury is $ b $ . The checker program will consider your answer correct, if .

3 0 0
0 1
-1 2
1 2

12.566370614359172464

4 1 -1
0 0
1 2
2 0
1 1

21.991148575128551812

In the first sample snow will be removed from that area: