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.File;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.Scanner;
import java.util.Vector;
import javafx.util.Pair;

public class A {
    PrintStream cout = new PrintStream(System.out);
    Scanner cin;
    final int MAX_LIMIT = 100 * 1000 + 100;
    final double eps = 1e-6;

    //Vector <Integer>[] arr = (Vector<Integer> []) new Vector[100]; 
    Point[] points = new Point[MAX_LIMIT];
    
    

    private boolean is_zero(double d){
        return Math.abs(d) <= eps;
    }
    
    private class Point implements Comparable<Point> {

        long x, y;

        public Point(long x, long y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(Point o) {
            int ret = Long.compare(this.y, o.y);
            if (ret != 0) {
                return ret;
            }
            return Long.compare(this.x, o.x);
        }

        public double dist(Point pp) {
            return Math.sqrt((pp.x - x) * (pp.x - x) + (pp.y - y) * (pp.y - y));
        }
        
        public Point minus(Point pp){
            return new Point(this.x - pp.x, this.y - pp.y);
        }

    }
    
    
    private class Line{ //Ax+By=C
        double A, B, C;
        public Line(double _A, double _B, double _C){
            A = _A;
            B = _B;
            C = _C;
        }
        public Line(){
        }
    }
    
    //right hand rule
    double cross(Point q, Point p1, Point p2){ //product of Q_P1 Q_P2
        p1 = p1.minus(q); 
        p2 = p2.minus(q); //to make A x B --> q = (0, 0) p1 = A p2 = B
        return p1.x*p2.y - p1.y*p2.x; //|A||B|sin(x)
    }

    double dot(Point q, Point p1, Point p2) { //product of Q_P1 P1_P2
        p2 = p2.minus(p1);
        //to make A.B --> q = (0, 0) p1 = A p2 = A + B
        p1 = p1.minus(q);
        //|A||B|cos(x)
        return p1.x * p2.x + p1.y * p2.y;
    }

    double LinePointDis(Point p1, Point p2, Point q, boolean isSegment) {
        // p1 and p2 are on the line
        double dist = p1.dist(p2);
        if (is_zero(dist)) {
            return 0.0;
        }
        double ret = cross(p1, p2, q) / dist;
        if (isSegment){
            //p1 is out of range
            if (dot(p1, p2, q) > 0) {
                return p2.dist(q); //the angle between p1p2, p2q less than 90
            }
            //p1 is out of range
            if (dot(p2, p1, q) > 0) {
                return p1.dist(q); //the angle between p2p1, p1q less than 90
            }
        }
        return Math.abs(ret);
    }

    Line point_to_line(Point p1, Point p2){
        Line ret = new Line();
        ret.A = p2.y - p1.y; //y2 - y1
        ret.B = p1.x - p2.x; //-(x2 - x1)
        ret.C = ret.A * p1.x + ret.B * p1.y; // C = A x X1 + B x Y1
        return ret;
    }

    void solve() {
        int n = cin.nextInt();
        Point p = new Point(cin.nextLong(), cin.nextLong());
        for (int i = 0; i < n; i++) {
            points[i] = new Point(cin.nextLong(), cin.nextLong());
        }

        double min = Double.MAX_VALUE;
        double max = Double.MIN_VALUE;
        for (int i = 0; i < n; i++) {
            double cur = LinePointDis(points[i], points[(i + 1)%n], p, true);
            double cur2 = points[i].dist(p);
            double cur3 = points[(i+1)%n].dist(p);
            
            min = Math.min(min, cur);
            min = Math.min(min, cur2);
            min = Math.min(min, cur3);
            max = Math.max(max, cur);
            max = Math.max(max, cur2);
            max = Math.max(max, cur3);
        }

        double ans = Math.PI * (max * max - min * min);
        cout.print(ans);
    }

    void run(String[] args) throws Exception {

        boolean is_local = args.length > 0 && args[0].equals("MASHREGHI");
        if (is_local) {//this is local host
            File inputFile = new File(System.getProperty("user.dir")
                    + "\\src\\in.in");
            cin = new Scanner(inputFile);
            cout.print(System.getProperty("user.dir") + "\\src\\"
                    + this.getClass().getName() + ".java\n"); //this is to be used when submitting code
        } else {
            cin = new Scanner(System.in);
        }

        solve();

        if (is_local) {
            cout.println();
        }
    }

    public static void main(String[] args) throws Exception {
        new A().run(args);
    }

}