CodeForces 614C Peter and Snow Blower【计算几何】

C. Peter and Snow Blower

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

Input

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 1 000 000 in their absolute value.

Output

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 .

Examples

input

3 0 0
0 1
-1 2
1 2

output

12.566370614359172464

input

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

output

21.991148575128551812

Note

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

题意：

按顺序给出一个多边形的各个顶点，另给出一个固定点p（点在多边形外部），问这个多边形绕着这个顶点旋转扫过的面积是多少

题解：

按常识可知，必定得到一个圆环，具体就是需要求小圆和大圆的半径，也就是多边形上距离p点最近的点和最远的点

1，距离p 最远的点必定是某一个顶点

2，距离p 最近的点必定是某一个顶点，或者是p点在某条边上的垂足，

然后就是计算了..........

第一次做这么复杂的计算几何，瞬间感觉再也不会做了....首先模板很重要，比赛当场写各种函数绝对会死，其要对各种情况分清楚讨论

有机会再优化一下，感觉代码好丑啊...

/*
    http://blog.csdn.net/liuke19950717
*/
#include
#include
const double pi=acos(-1.0);
const double eps=1e-8;
struct point
{
	double x,y;
}x[100005],p;
double Max(double x,double y)
{
	return x>y?x:y;
}
double Min(double x,double y)
{
	return x=l&&p.x<=r)
        {
            tp.x=p.x;tp.y=a.y;
            return tp;
        }
        else if(p.x=l&&p.y<=r)
        {
            tp.y=p.y;tp.x=a.x;
            return tp;
        }
        else if(p.y=l&&x<=r)
        {
            point tp;
            tp.x=x;tp.y=y;
            return tp;
        }
        else if(xb.x)
            {
                return b;
            }
            else
            {
                return a;
            }
        }
        else
        {
            if(a.x>b.x)
            {
                return a;
            }
            else
            {
                return b;
            }
        }
    }
}
int main()
{
	int n;
	//freopen("shuju.txt","r",stdin);
	while(~scanf("%d%lf%lf",&n,&p.x,&p.y))
	{
		double dismax=0;//最远距离
		for(int i=0;i