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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author whhone
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    TaskA solver = new TaskA();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskA {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
      int n = in.nextInt();
      Point origin = new Point(in.nextInt(), in.nextInt());
      Point pre, first, p;
      pre = first = new Point(in.nextInt(), in.nextInt());

      double mn, mx;
      mn = mx = origin.distance(first);

      for (int i = 1; i < n; i++) {
        p = new Point(in.nextInt(), in.nextInt());
        double d2 = origin.distance(p);
        mx = Math.max(mx, d2);
        mn = Math.min(mn, d2);
        Segment segment = new Segment(pre, p);
        mn = Math.min(mn, origin.distance(segment));
        pre = p;
      }
      mn = Math.min(mn, origin.distance(new Segment(first, pre)));
//    out.printf("%f %f %f %f %f\n", first.x, first.y, pre.x, pre.y, origin.distance(new Segment(first, pre)));
//    out.printf("%f %f\n", mn, mx);
      out.println((mx * mx - mn * mn) * Math.PI);
    }

  }

  static class OutputWriter extends PrintWriter {
    public OutputWriter(OutputStream stream) {
      super(stream);
    }

    public OutputWriter(Writer writer) {
      super(writer);
    }

  }

  static class Segment {
    public Point p;
    public Point q;

    public Segment(double x1, double y1, double x2, double y2) {
      this(new Point(x1, y1), new Point(x2, y2));
    }

    public Segment(Point point_1, Point point_2) {
      this.p = point_1;
      this.q = point_2;
    }

    public double length() {
      return p.distance(q);
    }

  }

  static class GeomConfig {
    static double epsilon = 1e-8;

    public static double getEpsilon() {
      return epsilon;
    }

  }

  static class Line {
    public double a;
    public double b;
    public double c;

    public Line(double a, double b, double c) {
      double t = Math.sqrt(a * a + b * b);
      this.a = a / t;
      this.b = b / t;
      this.c = c / t;
    }

    public Line(double x1, double y1, double x2, double y2) {
      this(y2 - y1, x1 - x2, y1 * x2 - x1 * y2);
    }

    public Line(Point a, Point b) {
      this(a.x, a.y, b.x, b.y);
    }

    public Line(Segment segment) {
      this(segment.p.x, segment.p.y, segment.q.x, segment.q.y);
    }

  }

  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), 32768);
      tokenizer = null;
    }

    public String nextLine() {
      try {
        return reader.readLine();
      } catch (IOException e) {
        throw new RuntimeException(e);
      }
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        tokenizer = new StringTokenizer(nextLine());
      }
      return tokenizer.nextToken();
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }

  }

  static class Point {
    public double x;
    public double y;

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

    public double distance2(Point point) {
      return (point.x - this.x) * (point.x - this.x) + (point.y - this.y) * (point.y - this.y);
    }

    public double distance(Point point) {
      return Math.sqrt(distance2(point));
    }

    public double distance(Line line) {
      return Math.abs(line.a * this.x + line.b * this.y + line.c);
    }

    public double distance(Segment segment) {
      double c = segment.length();
      double a = distance(segment.p);
      if (c < GeomConfig.getEpsilon()) {
        return a;
      }
      double b = distance(segment.q);
      if (b * b + c * c < a * a) {
        return b;
      }
      if (a * a + c * c < b * b) {
        return a;
      }
      return distance(new Line(segment));
    }

  }
}