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.awt.geom.Point2D;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;

import com.sun.javafx.geom.Line2D;

public class P613A_Peter_SnowBlower {
/* Sample
Input
3 0 0
-1 1
0 3
1 1

Output
21.9911485751

Answer
25.132741228718344928
*/	
	private static PrintWriter pw;
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(System.out);
		String textLine = br.readLine();
		String[] splitted = textLine.split("\\s+");
		int nVertices = Integer.parseInt(splitted[0]);
		double centerX = Double.parseDouble(splitted[1]);
		double centerY = Double.parseDouble(splitted[2]);
		double minDistanceSq = Double.POSITIVE_INFINITY;
		double maxDistanceSq = 0;
		double pointDistanceSq, lineDistanceSq;
		double x, y;
		double prevX = 0, prevY = 0;
		double answer = 0;
		double firstX = 0, firstY = 0;
		
		for (int i = 0; i < nVertices; i++) {
			textLine = br.readLine();
			splitted = textLine.split("\\s+");
			x = Double.parseDouble(splitted[0]);
			y = Double.parseDouble(splitted[1]);
			pointDistanceSq = Point2D.distanceSq(centerX, centerY, x, y);
			if (i == 0) {
				firstX = x;
				firstY = y;
				lineDistanceSq = pointDistanceSq;
			} else {
				lineDistanceSq = ptSegDistSq(x, y, prevX, prevY, centerX, centerY);
			}
			
			if (minDistanceSq > lineDistanceSq) {
				minDistanceSq = lineDistanceSq;
			}
			if (maxDistanceSq < pointDistanceSq) {
				maxDistanceSq = pointDistanceSq;
			}
			prevX = x;
			prevY = y;
		}
		
		if (nVertices > 1) {
			x = firstX;
			y = firstY;
			lineDistanceSq = ptSegDistSq(x, y, prevX, prevY, centerX, centerY);
			if (minDistanceSq > lineDistanceSq) {
				minDistanceSq = lineDistanceSq;
			}
			lineDistanceSq = ptSegDistSq(x, y, prevX, prevY, centerX, centerY);
		}
		
		answer = Math.PI * (maxDistanceSq - minDistanceSq);
		
		pw.printf("%.10f\n", answer);
		pw.close();
	}
	
    public static double ptSegDistSq(double x1, double y1,
            double x2, double y2,
            double px, double py)
	{
		// Adjust vectors relative to x1,y1
		// x2,y2 becomes relative vector from x1,y1 to end of segment
		x2 -= x1;
		y2 -= y1;
		// px,py becomes relative vector from x1,y1 to test point
		px -= x1;
		py -= y1;
		double dotprod = px * x2 + py * y2;
		double projlenSq;
		if (dotprod <= 0.0) {
			// px,py is on the side of x1,y1 away from x2,y2
			// distance to segment is length of px,py vector
			// "length of its (clipped) projection" is now 0.0
			projlenSq = 0.0;
		} else {
			// switch to backwards vectors relative to x2,y2
			// x2,y2 are already the negative of x1,y1=>x2,y2
			// to get px,py to be the negative of px,py=>x2,y2
			// the dot product of two negated vectors is the same
			// as the dot product of the two normal vectors
			px = x2 - px;
			py = y2 - py;
			dotprod = px * x2 + py * y2;
			if (dotprod <= 0.0) {
				// px,py is on the side of x2,y2 away from x1,y1
				// distance to segment is length of (backwards) px,py vector
				// "length of its (clipped) projection" is now 0.0
				projlenSq = 0.0;
			} else {
				// px,py is between x1,y1 and x2,y2
				// dotprod is the length of the px,py vector
				// projected on the x2,y2=>x1,y1 vector times the
				// length of the x2,y2=>x1,y1 vector
				projlenSq = dotprod * dotprod / (x2 * x2 + y2 * y2);
			}
		}
		// Distance to line is now the length of the relative point
		// vector minus the length of its projection onto the line
		// (which is zero if the projection falls outside the range
		// of the line segment).
		double lenSq = px * px + py * py - projlenSq;
		if (lenSq < 0f) {
			lenSq = 0f;
		}
		return lenSq;
	}
}