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.awt.*;
import java.awt.geom.*;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.Collector;

/**
 * Created by ribra on 11/15/2015.
 */
public class Main {

    private static InputReader sc = new InputReader(System.in);
    private static PrintWriter pw = new PrintWriter(System.out);




    public static void main(String [] args) {

        int n = sc.nextInt();
        Point2D p = new Point2D.Double((double) sc.nextInt(), (double) sc.nextInt());

        Point2D[] arr = new Point2D[n];
        for (int i = 0; i < n; i++) {
            arr[i] = new Point2D.Double((double) sc.nextInt(), (double) sc.nextInt());
        }


        double min = Double.MAX_VALUE;
        double max = Double.MIN_VALUE;

        for (int i = 0; i < n; i++) {
            int j = (i + 1) % n;
            Line2D line = new Line2D.Double(arr[i], arr[j]);

            min = Math.min(min, line.ptSegDist(p));
            min = Math.min(min, p.distance(arr[i]));
            min = Math.min(min, p.distance(arr[j]));

            max = Math.max(max, line.ptSegDist(p));
            max = Math.max(max, p.distance(arr[i]));
            max = Math.max(max, p.distance(arr[j]));
        }

        pw.print(Math.PI * (max * max - min * min));


        terminate();
    }




    public static void terminate() {
        pw.close();
    }


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

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

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }

    static class Graph {
        private int V;
        private int E;
        private Set<Integer>[] adj;

        public Graph(int V) {
            this.V = V;
            this.E = 0;
            adj = new HashSet[V];
            for (int i = 0; i < V; i++)
                adj[i] = new HashSet<>();
        }


        public int V() {
            return V;
        }

        public int E() {
            return E;
        }

        public void addEdge(int v, int w) {
            adj[v].add(w);
            adj[w].add(v);
            E++;
        }

        public Iterable<Integer> adj(int v) {
            return adj[v];
        }


        public static int degree(Graph g, int v) {
            int degree = 0;
            for (int w : g.adj(v)) degree++;
            return degree;
        }


        public static int maxDegree(Graph g) {
            int max = 0;
            for (int i = 0; i < g.V(); i++)
                max = Math.max(degree(g, i), max);
            return max;
        }


        public static int avgDegree(Graph g) {
            int sum = 0;
            for (int i = 0; i < g.V(); i++)
                sum += degree(g, i);
            return sum / g.V();
        }


        public static int avgDegreeEfficient(Graph g) {
            // g.E = sum degree of every graph
            // 2 * g.E - because if v is connected to w, then w is connected to v as well
            // and divide by number of vertices
            return 2 * g.E() / g.V();
        }

        public static int numberOfSelfLoops(Graph g) {
            int count = 0;
            for (int i = 0; i < g.V(); i++)
                for (int w : g.adj(i))
                    if (i == w) count++;
            return count / 2;
        }

        public String toString()
        {
            String s = V() + " vertices, " + E() + " edges\n";
            for (int v = 0; v < V(); v++)
            {
                s += v + ": ";
                for (int w : this.adj(v))
                    s += w + " ";
                s += "\n";
            }
            return s;
        }

    }
}