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:
/*
Keep solving problems.
*/

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

public class CFA {
    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    private static final long MOD = 1000 * 1000 * 1000 + 7;
    private static final int[] dx = {0, -1, 0, 1};
    private static final int[] dy = {1, 0, -1, 0};
    private static final String yes = "Yes";
    private static final String no = "No";

    void solve() throws IOException {
        int n = nextInt();
        int x0 = nextInt();
        int y0 = nextInt();
        int[] xs = new int[n];
        int[] ys = new int[n];
        for (int i = 0; i < n; i++) {
            xs[i] = nextInt() - x0;
            ys[i] = nextInt() - y0;
        }

        double max = 0.0;
        double min = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++) {
            double dist = Math.sqrt(1L * xs[i] * xs[i] + 1L * ys[i] * ys[i]);
            max = Math.max(max, dist);
            min = Math.min(min, dist);
        }

        for (int i = 0; i < n; i++) {
            int x1 = xs[i];
            int y1 = ys[i];
            int x2 = xs[(i + 1) % n];
            int y2 = ys[(i + 1) % n];
            if (check(x1, y1, x2, y2)) {
                double d1 = findDist(x1, y1, x2, y2);
                double d2 = findDist(x1, y1, 0, 0);
                double d3 = findDist(x2, y2, 0, 0);
                double s = (d1 + d2 + d3) / 2;
                double area = Math.sqrt(s * (s - d1) * (s - d2) * (s - d3));
                double h = 2 * area / d1;
                min = Math.min(min, h);
            }
        }

        double res = Math.PI * (max + min) * (max - min);
        formatPrint(res);
    }

    boolean check(int x1, int y1, int x2, int y2) {
        if (1L * x1 * y2 == 1L * x2 * y1) {
            return false;
        }
        long dx1 = x2 - x1;
        long dy1 = y2 - y1;
        long dx2 = 0 - x1;
        long dy2 = 0 - y1;
        if (dx1 * dx2 + dy1 * dy2 < 0) {
            return false;
        }

        dx1 = x1 - x2;
        dy1 = y1 - y2;
        dx2 = 0 - x2;
        dy2 = 0 - y2;
        return dx1 * dx2 + dy1 * dy2 >= 0;
    }

    double findDist(int x1, int y1, int x2, int y2) {
        long dx = Math.abs(x1 - x2);
        long dy = Math.abs(y1 - y2);
        return Math.sqrt(dx * dx + dy * dy);
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }

    long gcd(long a, long b) {
        while(a != 0 && b != 0) {
            long c = b;
            b = a % b;
            a = c;
        }
        return a + b;
    }

    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    private void formatPrint(double val) {
        System.out.format("%.9f%n", val);
    }
    public CFA() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFA();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}