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.IOException;
import java.io.UncheckedIOException;
import java.math.BigDecimal;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            APeterAndSnowBlower solver = new APeterAndSnowBlower();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class APeterAndSnowBlower {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            Point2 center = new Point2(in.readInt(), in.readInt());
            Point2 last = null;
            double maxR = -1;
            double minR = (long) 1e18;
            Point2 first = null;
            for (int i = 0; i < n; i++) {
                Point2 cur = new Point2(in.readInt(), in.readInt());
                double r = Point2.dist(center, cur);
                maxR = Math.max(r, maxR);
                minR = Math.min(r, minR);

                if (last != null) {
                    Line2 line = new Line2(last, cur);
                    Point2 pt = line.projection(center);
                    if (Point2.onSegment(last, cur, pt)) {
                        minR = Math.min(minR, Point2.dist(pt, center));
                    }
                } else {
                    first = cur;
                }

                last = cur;
            }
            Line2 line = new Line2(last, first);
            Point2 pt = line.projection(center);
            if (Point2.onSegment(last, first, pt)) {
                minR = Math.min(minR, Point2.dist(pt, center));
            }

            double ans = (maxR * maxR - minR * minR) * Math.PI;
            out.println(ans);
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class Line2 {
        public Point2 vec;
        public double c;

        public Line2(Point2 vec, double c) {
            this.vec = vec;
            this.c = c;
        }

        public Line2(double a, double b, double c) {
            this(new Point2(b, -a), c);
        }

        public Line2(Point2 a, Point2 b) {
            this.vec = Point2.minus(b, a);
            this.c = Point2.cross(vec, a);
        }

        private double side0(Point2 pt) {
            return Point2.cross(vec, pt) - c;
        }

        public Point2 projection(Point2 pt) {
            double factor = side0(pt) / vec.square();
            return new Point2(pt.x - (-vec.y * factor), pt.y - vec.x * factor);
            //return Point2.minus(pt, Point2.mul(vec.perpendicular(), side0(pt) / vec.square()));
        }

        public String toString() {
            return -vec.y + "x + " + vec.x + "y = " + c;
        }

    }

    static class Point2 implements Cloneable {
        public final double x;
        public final double y;

        public Point2(double x, double y) {
            this.x = x;
            this.y = y;
        }

        public Point2() {
            this(0, 0);
        }

        public double square() {
            return dot(this, this);
        }

        public static Point2 minus(Point2 a, Point2 b) {
            return new Point2(a.x - b.x, a.y - b.y);
        }

        public static double dot(Point2 a, Point2 b) {
            return a.x * b.x + a.y * b.y;
        }

        public static double dot(double x1, double y1, double x2, double y2) {
            return x1 * x2 + y1 * y2;
        }

        public static double cross(Point2 a, Point2 b) {
            return a.x * b.y - a.y * b.x;
        }

        public static int orient(Point2 a, Point2 b, Point2 c) {
            return GeoConstant.sign(GeoConstant.cross(b.x - a.x, b.y - a.y, c.x - a.x, c.y - a.y));
        }

        public static boolean inDisk(Point2 a, Point2 b, Point2 c) {
            return GeoConstant.sign(dot(a.x - c.x, a.y - c.y, b.x - c.x, b.y - c.y)) <= 0;
        }

        public static boolean onSegment(Point2 a, Point2 b, Point2 c) {
            return orient(a, b, c) == 0 && inDisk(a, b, c);
        }

        public static double dist2(Point2 a, Point2 b) {
            double dx = a.x - b.x;
            double dy = a.y - b.y;
            return dx * dx + dy * dy;
        }

        public static double dist(Point2 a, Point2 b) {
            return Math.sqrt(dist2(a, b));
        }

        public Point2 clone() {
            try {
                return (Point2) super.clone();
            } catch (CloneNotSupportedException e) {
                throw new RuntimeException(e);
            }
        }

        public String toString() {
            return String.format("(%.6f, %.6f)", x, y);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 1 << 13;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(double c) {
            cache.append(new BigDecimal(c).toPlainString());
            afterWrite();
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput println(double c) {
            return append(c).println();
        }

        public FastOutput println() {
            return append(System.lineSeparator());
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class GeoConstant {
        public static final double PREC = 1e-12;

        public static boolean isZero(double x) {
            return -PREC <= x && x <= PREC;
        }

        public static int sign(double x) {
            return isZero(x) ? 0 : x < 0 ? -1 : 1;
        }

        public static double cross(double x1, double y1, double x2, double y2) {
            return x1 * y2 - y1 * x2;
        }

    }
}