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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author AlexFetisov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA_339 solver = new TaskA_339();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA_339 {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            Point p = new Point(in);
            double minDst = Double.MAX_VALUE, maxDst = Double.MIN_VALUE;

            Point A = new Point(in);
            minDst = DoubleUtils.min(minDst, p.distanceTo(A));
            maxDst = DoubleUtils.max(maxDst, p.distanceTo(A));
            Point M = A;
            for (int i = 1; i < n; ++i) {
                Point B = new Point(in);
                minDst = DoubleUtils.min(minDst, p.distanceTo(B));
                maxDst = DoubleUtils.max(maxDst, p.distanceTo(B));

                minDst = DoubleUtils.min(minDst, new Segment(A, B).distanceTo(p));
                maxDst = DoubleUtils.max(maxDst, new Segment(A, B).distanceTo(p));
                A = B;
            }

            Point B = M;
            minDst = DoubleUtils.min(minDst, new Segment(A, B).distanceTo(p));
            maxDst = DoubleUtils.max(maxDst, new Segment(A, B).distanceTo(p));

            out.println(Math.PI * (DoubleUtils.sqr(maxDst) - DoubleUtils.sqr(minDst)));
        }

    }

    static class Segment {
        public final Point a;
        public final Point b;
        private double distance = Double.NaN;
        private Line line = null;

        public Segment(Point a, Point b) {
            this.a = a;
            this.b = b;
        }

        public double length() {
            if (Double.isNaN(distance)) {
                distance = a.distanceTo(b);
            }
            return distance;
        }

        public double distanceTo(Point point) {
            double length = length();
            double left = point.distanceTo(a);
            if (DoubleUtils.compareTo(length, 0) == 0) {
                return left;
            }
            double right = point.distanceTo(b);
            if (left * left > right * right + length * length) {
                return right;
            }
            if (right * right > left * left + length * length) {
                return left;
            }
            return point.distanceTo(line());
        }


        public String toString() {
            return a.toString() + ", " + b.toString();
        }

        public Line line() {
            if (line == null) {
                line = a.line(b);
            }
            return line;
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer stt;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
        }

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

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

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

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

    }

    static class DoubleUtils {
        public static final double EPS = 1e-10;

        public static double sqr(double x) {
            return x * x;
        }

        public static int compareTo(double a, double b) {
            if (doubleEqual(a, b)) {
                return 0;
            }
            if (a < b) {
                return -1;
            }
            return 1;
        }

        private static boolean doubleEqual(double a, double b) {
            return Math.abs(a - b) < EPS;
        }

        public static double sqrt(double a) {
            if (compareTo(a, 0) < 0) {
                System.exit(1);
            }
            if (a < 0) return 0;
            return Math.sqrt(a);
        }

        public static double min(double a, double b) {
            return compareTo(a, b) < 0 ? a : b;
        }

        public static double max(double a, double b) {
            return compareTo(a, b) > 0 ? a : b;
        }

        public static double hypot(double a, double b) {
            return sqrt(sqr(a) + sqr(b));
        }

    }

    static class Line {
        public final double a;
        public final double b;
        public final double c;
        public Point p1;
        public Point p2;
        boolean hasPoints;


        public int hashCode() {
            double res = a * 1e50 + b * 1e25 + c;
            return (int) res;
        }

        public Line(Point p, double angle) {
            a = Math.sin(angle);
            b = -Math.cos(angle);
            c = -p.x * a - p.y * b;
            p1 = p2 = null;
            hasPoints = false;
        }

        public Line(double a, double b, double c) {
            double h = DoubleUtils.hypot(a, b);
            this.a = a / h;
            this.b = b / h;
            this.c = c / h;
            hasPoints = false;
        }

        public Line(Point p1, Point p2) {
            double a = p2.y - p1.y;
            double b = p1.x - p2.x;
            double c = -(p1.x * a + p1.y * b);
            double h = DoubleUtils.hypot(a, b);
            this.a = a / h;
            this.b = b / h;
            this.c = c / h;
            hasPoints = true;
        }

        public boolean parallel(Line other) {
            return DoubleUtils.compareTo(Math.abs(a * other.b - b * other.a), 0) == 0;
        }


        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Line line = (Line) o;

            if (!parallel(line)) return false;
            if (Math.abs(a * line.c - c * line.a) > DoubleUtils.EPS || Math.abs(b * line.c - c * line.b) > DoubleUtils.EPS)
                return false;

            return true;
        }

    }

    static class Point implements Comparable<Point> {
        public double x;
        public double y;

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

        public Line line(Point other) {
            if (equals(other))
                return null;
            double a = other.y - y;
            double b = x - other.x;
            double c = -a * x - b * y;
            return new Line(a, b, c);
        }

        public Point() {
            this.x = 0;
            this.y = 0;
        }

        public Point(InputReader in) {
            this.x = in.nextDouble();
            this.y = in.nextDouble();
        }


        public String toString() {
            return "(" + x + ", " + y + " )";
        }


        public boolean equals(Object o) {
            Point p = (Point) o;
            return DoubleUtils.compareTo(x, p.x) == 0 && DoubleUtils.compareTo(y, p.y) == 0;
        }

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


        public int hashCode() {
            int result;
            long temp;
            temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
            result = (int) (temp ^ (temp >>> 32));
            temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
            result = 31 * result + (int) (temp ^ (temp >>> 32));
            return result;
        }

        public Point sub(Point p) {
            return new Point(x - p.x, y - p.y);
        }

        public double dotProduct(Point p) {
            return x * p.x + y * p.y;
        }

        public double length() {
            return DoubleUtils.sqrt(dotProduct(this));
        }

        public double distanceTo(Point p) {
            return sub(p).length();
        }


        public int compareTo(Point o) {
            int temp = DoubleUtils.compareTo(x, o.x);
            if (temp == 0) {
                return DoubleUtils.compareTo(y, o.y);
            }
            return temp;
        }

    }
}