Problem: 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 (<image>), 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 <image>.

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:

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class A613 {
public static void main(String[] args) throws IOException {
	input.init(System.in);
	PrintWriter out = new PrintWriter(System.out);
	int n = input.nextInt();
	Point p = new Point(input.nextDouble(), input.nextDouble());
	double closest = 1e18, farthest = 0;
	Point[] poly = new Point[n];
	for(int i = 0; i<n; i++) poly[i] = new Point(input.nextDouble(), input.nextDouble());
	for(int i = 0; i<n; i++)
	{
		closest = Math.min(closest, plDist(poly[i], poly[(i+1)%n], p));
		farthest = Math.max(farthest, p.dist(poly[i]));
	}
	out.println(Math.PI * ((farthest * farthest) - (closest*closest)));
	out.close();
}
//Point-line distance
//Commented code for point-segment distance
//Input: Line from A to B, point to be tested p
public static double plDist(Point a, Point b, Point p){
Point c = p.minus(a);
Point d = b.minus(a);
if(c.dot(d) < 0)
	return p.dist(a);
if(p.minus(b).dot(d.mult(-1)) < 0)
	return p.dist(b);
return Math.abs(c.cross(d))/d.mag();
}
public static class Point implements Comparable<Point>
{
	double x, y; //x and y represent the coordinates of a point or the components of a vector
	public Point(double myx, double myy)
	{
		x = myx; y = myy;
	}
	//returns this + that
	public Point plus(Point p)
	{
		return new Point(this.x+p.x, this.y+p.y);
	}
	//returns this - that
	public Point minus(Point p)
	{
		return new Point(this.x-p.x,this.y-p.y);
	}
	//scales vector by multiple of d
	public Point mult(double d)
	{
		return new Point(this.x*d, this.y*d);
	}
	//returns this (dot) that
	public double dot(Point p)
	{
		return this.x*p.x + this.y*p.y;
	}
	//returns this x that
	public double cross(Point p)
	{
		return this.x*p.y - this.y*p.x;
	}
	//returns magnitude squared of vector
	public double magSquared()
	{
		return this.x*this.x + this.y*this.y;
	}
	//returns magnitude of vector
	public double mag()
	{
		return Math.sqrt(magSquared());
	}
	//returns a vector normal to this one
	public Point normal()
	{
		return new Point(this.y/mag(), -1*this.x/mag());
	}
	//rotates vector clockwise by angle theta
	public Point rotate(double theta)
	{
		double nx = x*Math.cos(theta) - y*Math.sin(theta);
		double ny = x*Math.sin(theta) + y*Math.cos(theta);
		return new Point(nx, ny);
	}
	//returns unit vector
	public Point normalize()
	{
		double d = mag();
		return new Point(x/d, y/d);
	}
	public double dist(Point p)
	{
		return this.minus(p).mag();
	}
	public double dist2(Point p)
	{
		return this.minus(p).magSquared();
	}
	public int compareTo(Point p){
		if(p.x == x)
			return (int)Math.signum(y-p.y);
		return (int)Math.signum(x-p.x);	
	}
	public Point orthoCCW()
	{ //Rotate 90 degrees counter-clockwise
		return new Point(-y, x);
	}
	public Point orthoCW()
	{ //Rotate 90 degrees clockwise
		return new Point(y, -x);
	}
}
public static class input {
	static BufferedReader reader;
	static StringTokenizer tokenizer;

	static void init(InputStream input) {
		reader = new BufferedReader(new InputStreamReader(input));
		tokenizer = new StringTokenizer("");
	}

	static String next() throws IOException {
		while (!tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(reader.readLine());
		return tokenizer.nextToken();
	}

	static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	static long nextLong() throws IOException {
		return Long.parseLong(next());
	}
}
}