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.*;
import java.util.InputMismatchException;


public class Main {
    private static InputReader ir;
    private static OutputWriter ow;
    final static int INF = Integer.MAX_VALUE;

    public static void main(String[] args) throws Exception {
        initS();
        //initF("INPUT.TXT", "OUTPUT.TXT");
        task();
        exit();
    }

    private static Double getDD(int x1, int y1, int x2, int y2) {
        if (x1 == x2 && y1 != y2) {
            if (y1 * y2 <= 0)
                return (double) x1 * x1;
            else return null;
        }

        if (x1 == x2)
            return getDD(x1, y1);

        int x = x2 - x1;
        int y = y2 - y1;

        double s1 = (double) x * x1 + (double) y * y1;
        double s2 = (double) x * x2 + (double) y * y2;

        if (s1 * s2 <= 0) {
            double k = (double) y / x;
            double b = y2 - k * x2;

            return (y - k * x - b) * (y - k * x - b) / (1 + k * k);
        } else
            return null;
    }

    private static Double getDD(int x, int y) {
        return (double) x * x + (double) y * y;
    }


    private static void task() throws Exception {
        int n = ir.nextInt();
        int px = ir.nextInt(), py = ir.nextInt();
        int[] x = new int[n];
        int[] y = new int[n];

        for (int i = 0; i < n; ++i) {
            x[i] = ir.nextInt() - px;
            y[i] = ir.nextInt() - py;
        }

        Double RR = getDD(x[0], y[0]), rr = RR;

        for (int i = 0; i < n; ++i) {
            Double dds = getDD(x[i], y[i], x[(i + 1) % n], y[(i + 1) % n]);
            Double ddp = getDD(x[i], y[i]);
            RR = Math.max(ddp, RR);
            rr = Math.min(rr, ddp);
            if (dds != null)
                rr = Math.min(rr, dds);
        }
        ow.print(String.valueOf(Math.PI * (RR - rr)));
    }

    private static void initS() throws IOException {
        ir = new InputReader(System.in);
        ow = new OutputWriter(System.out);
    }

    private static void initF(String inName, String outName) throws IOException {
        ir = new InputReader(new FileInputStream(inName));
        ow = new OutputWriter(new FileOutputStream(outName));
    }

    private static void exit() throws Exception {
        ir.close();
        ow.close();
    }
}


class InputReader implements AutoCloseable {
    private final InputStream in;
    private int capacity;
    private byte[] buffer;
    private int len = 0;
    private int cur = 0;

    public InputReader(InputStream stream) {
        this(stream, 100_000);
    }

    public InputReader(InputStream stream, int capacity) {
        this.in = stream;
        this.capacity = capacity;
        buffer = new byte[capacity];
    }

    private int read() {
        if (cur >= len) {
            try {
                cur = 0;
                len = in.read(buffer, 0, capacity);
                if (len <= 0)
                    return -1;
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        return buffer[cur++];
    }

    private boolean isSpace(int c) {
        return c == ' ' || isEscape(c);
    }

    private boolean isEscape(int c) {
        return c == '\n' || c == '\t' || c == '\r' || c == -1;
    }

    private int readSkipSpace() {
        int c;
        do {
            c = read();
        } while (isSpace(c));
        return c;
    }

    int nextInt() {
        int c = readSkipSpace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res = res * 10 + c - '0';
            c = read();
        } while (!isSpace(c));
        res *= sgn;
        return res;
    }

    public long nextLong() {
        int c = readSkipSpace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res = res * 10 + c - '0';
            c = read();
        } while (!isSpace(c));
        res *= sgn;
        return res;
    }

    int nextChar() {
        return readSkipSpace();
    }

    String nextLine() {
        StringBuilder res = new StringBuilder();
        int c = readSkipSpace();
        do {
            res.append((char) (c));
            c = read();
        } while (!isEscape(c));
        return res.toString();
    }

    @Override
    public void close() throws Exception {
        in.close();
    }
}


class OutputWriter implements Flushable, AutoCloseable {
    private byte[] buf;
    private int capacity;
    private int count;
    private OutputStream out;

    public OutputWriter(OutputStream stream) {
        out = stream;
        capacity = 10_000;
        buf = new byte[capacity];
    }

    public OutputWriter(OutputStream stream, int capacity) {
        if (capacity <= 0)
            throw new IllegalArgumentException("capacity <= 0");
        out = stream;
        this.capacity = capacity;
        buf = new byte[capacity];
    }

    public void write(int b) throws IOException {
        if (count >= buf.length)
            flushBuffer();
        buf[count++] = (byte)b;
    }

    public void write(byte[] bytes, int off, int len) throws IOException {
        if (len >= buf.length) {
            flushBuffer();
            out.write(bytes, off, len);
            return;
        }
        if (len > buf.length - count)
            flushBuffer();
        System.arraycopy(bytes, off, buf, count, len);
        count += len;
    }

    public void write(byte[] bytes) throws IOException {
        write(bytes, 0, bytes.length);
    }

    public void print(int i) throws IOException {
        print(String.valueOf(i));
    }

    public void print(long l) throws IOException {
        print(String.valueOf(l));
    }

    public void print(String str) throws IOException {
        write(str.getBytes());
    }

    public void println() throws IOException {
        print("\n");
    }

    public void println(String str) throws IOException {
        print(str);
        print("\n");
    }

    public void println(int i) throws IOException {
        print(i);
        println();
    }

    public void println(long l) throws IOException {
        print(l);
        println();
    }

    public void print(String separator, Object... objects) throws IOException {
        if (objects == null) return;
        for (int i = 0; i < objects.length; ++i) {
            if (i != 0 && separator != null) print(separator);
            print(objects[i].toString());
        }
    }

    private void flushBuffer() throws IOException {
        if (count > 0) {
            out.write(buf, 0, count);
            count = 0;
        }
    }

    @Override
    public void flush() throws IOException {
        flushBuffer();
        out.flush();
    }

    @Override
    public void close() throws Exception {
        flush();
        out.close();
    }
}