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:

//package javaapplication163;


import java.io.*;
import java.util.*;

public class C {

    public static void main(String[] args) {
        CIO io = new CIO();
        try {
            Csolver solver = new Csolver(io);
        } finally {
            io.close();
        }
    }

}

class Csolver {

    public Csolver(CIO io) {
        int n = io.nextInt();
        long[] x = new long[n+1];
        long[] y = new long[n+1];
        x[0] = io.nextInt();
        y[0] = io.nextInt();
        double minDistance = Double.POSITIVE_INFINITY;
        double maxDistance = Double.NEGATIVE_INFINITY;
        for (int i=1; i<=n; i++) {
            x[i] = io.nextInt();
            y[i] = io.nextInt();
            double c = Math.pow(x[i] - x[0], 2);
            double b = Math.pow(y[i] - y[0], 2);
            double distPisteeseen = Math.sqrt(c + b);
            maxDistance = Math.max(distPisteeseen, maxDistance);
            minDistance = Math.min(distPisteeseen, minDistance);
            
            if (i==1) continue;
            // tee suora edellisen kanssa, siitäkin mindistance suora -> origo
            double m = minDistFromPointToLineSegment(x[0], y[0], x[i], y[i], x[i-1], y[i-1]);
            minDistance = Math.min(m, minDistance);
        }
        // tee suora viimeinen->ensimmäinen, siitäkin mindistance suora->origo
        double m = minDistFromPointToLineSegment(x[0], y[0], x[n], y[n], x[1], y[1]);
        minDistance = Math.min(m, minDistance);
        
        double isompiYmpyra = Math.PI * Math.pow(maxDistance, 2);
        double pikkuYmpyra = Math.PI * Math.pow(minDistance, 2);
        io.println(isompiYmpyra - pikkuYmpyra);
    }
    
    double dist2(long x1, long y1, long x2, long y2) {
        return Math.pow((x1 - x2), 2) + Math.pow((y1 - y2), 2);
    }
    
    double dist2(long x1, long y1, double x2, double y2) {
        return Math.pow((x1 - x2), 2) + Math.pow((y1 - y2), 2);
    }
    
    double distToSegmentSquared(long point_x, long point_y, long x1, long y1, long x2, long y2) {
        double l2 = dist2(x1,y1,x2,y2);
        if (l2 == 0) return dist2(point_x, point_y, x1, y1);
        double t = ((point_x - x1) * (x2 - x1) + (point_y - y1) * (y2 - y1)) / l2;
        if (t < 0) return dist2(point_x, point_y, x1, y1);
        if (t > 1) return dist2(point_x, point_y, x2, y2);
        
        double com_x = x1 + t * (x2 - x1);
        double com_y = y1 + t * (y2 - y1);
        return dist2(point_x, point_y, com_x, com_y);
    }
    
    double minDistFromPointToLineSegment(long point_x, long point_y, long x1, long y1, long x2, long y2) {
        return Math.sqrt(distToSegmentSquared(point_x, point_y, x1, y1, x2, y2));
    }
    
}

class CIO extends PrintWriter {
    private InputStreamReader r;
    private static final int BUFSIZE = 1 << 15;
    private char[] buf;
    private int bufc;
    private int bufi;
    private StringBuilder sb;

    public CIO() {
            super(new BufferedOutputStream(System.out));
            r = new InputStreamReader(System.in);

            buf = new char[BUFSIZE];
            bufc = 0;
            bufi = 0;
            sb = new StringBuilder();
    }

    private void fillBuf() throws IOException {
            bufi = 0;
            bufc = 0;
            while(bufc == 0) {
                    bufc = r.read(buf, 0, BUFSIZE);
                    if(bufc == -1) {
                            bufc = 0;
                            return;
                    }
            }
    }

    private boolean pumpBuf() throws IOException {
            if(bufi == bufc) {
                    fillBuf();
            }
            return bufc != 0;
    }

    private boolean isDelimiter(char c) {
            return c == ' ' || c == '\t' || c == '\n' || c == '\r' || c == '\f';
    }

    private void eatDelimiters() throws IOException {
            while(true) {
                    if(bufi == bufc) {
                            fillBuf();
                            if(bufc == 0) throw new RuntimeException("IO: Out of input.");
                    }

                    if(!isDelimiter(buf[bufi])) break;
                    ++bufi;
            }
    }

    public String next() {
            try {
                    sb.setLength(0);

                    eatDelimiters();
                    int start = bufi;

                    while(true) {
                            if(bufi == bufc) {
                                    sb.append(buf, start, bufi - start);
                                    fillBuf();
                                    start = 0;
                                    if(bufc == 0) break;
                            }

                            if(isDelimiter(buf[bufi])) break;
                            ++bufi;
                    }

                    sb.append(buf, start, bufi - start);

                    return sb.toString();
            } catch(IOException e) {
                    throw new RuntimeException("IO.next: Caught IOException.");
            }
    }

    public int nextInt() {
            try {
                    int ret = 0;

                    eatDelimiters();

                    boolean positive = true;
                    if(buf[bufi] == '-') {
                            ++bufi;
                            if(!pumpBuf()) throw new RuntimeException("IO.nextInt: Invalid int.");
                            positive = false;
                    }

                    boolean first = true;
                    while(true) {
                            if(!pumpBuf()) break;
                            if(isDelimiter(buf[bufi])) {
                                    if(first) throw new RuntimeException("IO.nextInt: Invalid int.");
                                    break;
                            }
                            first = false;

                            if(buf[bufi] >= '0' && buf[bufi] <= '9') {
                                    if(ret < -214748364) throw new RuntimeException("IO.nextInt: Invalid int.");
                                    ret *= 10;
                                    ret -= (int)(buf[bufi] - '0');
                                    if(ret > 0) throw new RuntimeException("IO.nextInt: Invalid int.");
                            } else {
                                    throw new RuntimeException("IO.nextInt: Invalid int.");
                            }

                            ++bufi;
                    }

                    if(positive) {
                            if(ret == -2147483648) throw new RuntimeException("IO.nextInt: Invalid int.");
                            ret = -ret;
                    }

                    return ret;
            } catch(IOException e) {
                    throw new RuntimeException("IO.nextInt: Caught IOException.");
            }
    }

    public long nextLong() {
            try {
                    long ret = 0;

                    eatDelimiters();

                    boolean positive = true;
                    if(buf[bufi] == '-') {
                            ++bufi;
                            if(!pumpBuf()) throw new RuntimeException("IO.nextLong: Invalid long.");
                            positive = false;
                    }

                    boolean first = true;
                    while(true) {
                            if(!pumpBuf()) break;
                            if(isDelimiter(buf[bufi])) {
                                    if(first) throw new RuntimeException("IO.nextLong: Invalid long.");
                                    break;
                            }
                            first = false;

                            if(buf[bufi] >= '0' && buf[bufi] <= '9') {
                                    if(ret < -922337203685477580L) throw new RuntimeException("IO.nextLong: Invalid long.");
                                    ret *= 10;
                                    ret -= (long)(buf[bufi] - '0');
                                    if(ret > 0) throw new RuntimeException("IO.nextLong: Invalid long.");
                            } else {
                                    throw new RuntimeException("IO.nextLong: Invalid long.");
                            }

                            ++bufi;
                    }

                    if(positive) {
                            if(ret == -9223372036854775808L) throw new RuntimeException("IO.nextLong: Invalid long.");
                            ret = -ret;
                    }

                    return ret;
            } catch(IOException e) {
                    throw new RuntimeException("IO.nextLong: Caught IOException.");
            }
    }

    public double nextDouble() {
            return Double.parseDouble(next());
    }

}