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.*;
import java.math.*;
import static java.lang.Math.*;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.Double.parseDouble;
import static java.lang.String.*;
   

public class Main {
            
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
                                            //(new FileReader("input.in"));
        StringBuilder out = new StringBuilder();
        StringTokenizer tk;
        Reader.init(System.in);
        //PrintWriter pw = new PrintWriter("output.out", "UTF-8");
        
        double mn = Double.MAX_VALUE,mx = Double.MIN_VALUE;
        
        tk = new StringTokenizer(in.readLine());
        int n = parseInt(tk.nextToken());
        double x = parseDouble(tk.nextToken()), y = parseDouble(tk.nextToken());
        
        double x1,y1;
        point [] p = new point[n];
        int i;
        double d;
        point pnt = new point(x,y),p1,p2;
        
        for(i=0; i<n; i++) {
            tk = new StringTokenizer(in.readLine());
            x1 = parseDouble(tk.nextToken());
            y1 = parseDouble(tk.nextToken());
            
            p[i] = new point(x1,y1);
            
            d = hypot(x-x1, y-y1);
            
            mn = min(mn, d);
            mx = max(mx, d);
            
            
            if(i>0) {
                d = distToSegment(pnt, p[(i-1+n)%n], p[i]);
                mn = min(mn, d);
                mx = max(mx, d);
            }            
        }
        
        d = distToSegment(pnt, p[0], p[n-1]);
        mn = min(mn, d);
        mx = max(mx, d);
        
        System.out.println(PI*mx*mx-PI*mn*mn);
    }
       
    public static double distToSegment(point p,point a,point b) {
        vector ap = new vector(a,p), ab = new vector(a,b);
        double u = dot(ap,ab)/norm_sq(ab);
        if(u < 0.0)
            return hypot(p.x-a.x, p.y-a.y);
        if(u > 1.0)
            return hypot(p.x-b.x, p.y-b.y);
        return distToLine(p,a,b);
    }
    
    public static double distToLine(point p,point a,point b) {
        vector ap = new vector(a,p), ab = new vector(a,b);
        double u = dot(ap,ab)/norm_sq(ab);
        point c = translate(a, scale(ab,u));
        return hypot(p.x-c.x, p.y-c.y);
    }
    
    static class point {
        double x,y;
        
        public point(double x,double y) {
            this.x = x;
            this.y = y;
        }
    }
    
    static class vector {
        double x,y;
        
        public vector(point a,point b) {
            this.x = b.x-a.x;
            this.y = b.y-a.y;
        }
    }
    
    static double dot(vector a,vector b) {
        return a.x*b.x+a.y*b.y;
    }
    
    static double norm_sq(vector v) {
        return v.x*v.x+v.y*v.y;
    }
    
    static vector scale(vector v,double s) {
        v.x *= s;
        v.y *= s;
        return v;
    }
    
    static point translate(point p,vector v) {
        return new point(p.x+v.x, p.y+v.y);
    }
    
}

class Tools {
    
    public static boolean next_permutation(int [] p,int len) {
        int a =len-2;
        while(a>=0 && p[a]>=p[a+1])
            a--;
        
        if(a==-1)
            return false;
        
        int b = len-1;
        while(p[b]<=p[a])
            b--;
        
        p[a] += p[b];
        p[b] = p[a] - p[b];
        p[a] -= p[b];
        
        for(int i=a+1, j=len-1; i<j; i++,j--) {
            p[i] += p[j];
            p[j] = p[i]-p[j];
            p[i] -= p[j];
        }
        
        return true;
    }
    
}

class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) throws UnsupportedEncodingException {
        reader = new BufferedReader(
                     new InputStreamReader(input, "UTF-8") );
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    
    static String nextLine() throws IOException {
        return reader.readLine();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
    
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
}