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.PrintWriter;
import java.io.PrintStream;
import java.io.BufferedInputStream;
import java.util.concurrent.Callable;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		BufferedInputStream in = new BufferedInputStream(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskA {
		public void solve(int testNumber, BufferedInputStream _in, PrintWriter out) {

			InputReader in = new InputReader(_in);
			long startTime = System.currentTimeMillis();
			int nt = 1;
			Task t = new Task(1);
			t.readInput(in);
			t.call();
			t.writeOutput(out);
			in.close();
			System.err.println("Time: " + (System.currentTimeMillis() - startTime) + " miliseconds");
		}

	}

	static class Task implements Callable<Task> {
		Point p;
		Polygon poly = new Polygon();
		double RE = 0;
		int testNumber;

		public void readInput(InputReader in) {
	/* read input here */
			int n = in.nextInt();
			p = new Point(in.nextInt(), in.nextInt());

			for (int i = 0; i < n; ++i) {
				poly.lp.add(new Point(in.nextInt(), in.nextInt()));
			}

		}

		public Task call() {
	/* process main algorithm here */
			double mx = Double.MIN_VALUE;

			double tmp = 0;
			for (int i = 0; i < poly.lp.size(); ++i) {
				tmp = poly.lp.get(i).dist(p);
				if (tmp > mx) {
					mx = tmp;

				}
			}

			double min = Double.MAX_VALUE;
			for (int i = 0; i < poly.lp.size(); ++i) {
				int ni = poly.next(i);
				Line seg = Line.makeLine(poly.lp.get(i), poly.lp.get(ni), true);
				tmp = seg.distSegment(p);
				if (tmp < min) {
					min = tmp;
				}
			}

			RE = (mx * mx - min * min) * Math.PI;

			System.err.println("Test case: " + testNumber + " done!");
			return this;
		}

		public void writeOutput(PrintWriter out) {
			out.println(String.format("%.30f", RE));
		}

		Task(int testNumber) {
			this.testNumber = testNumber;
		}

	}

	static class Polygon {
		public ArrayList<Point> lp = new ArrayList<>();

		int next(int i) {
			return i == lp.size() - 1 ? 0 : i + 1;
		}


		public String toString() {
			return "[" + lp + "]";
		}

	}

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

		public InputReader(BufferedInputStream 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());
		}

		public void close() {
			try {
				if (reader != null)
					reader.close();
			} catch (Exception ex) {
				throw new RuntimeException(ex);
			}
		}

	}

	static class Point implements Comparable<Point> {
		public long x;
		public long y;

		public Point(Point o) {
			this.x = o.x;
			this.y = o.y;

		}

		public Point(long x, long y) {
			super();

			this.x = x;
			this.y = y;
		}

		public boolean isZeroPoint() {
			return x == 0 && y == 0;
		}


		public int compareTo(Point o2) {
			int t = Long.compare(y, o2.y);
			if (t != 0) return t;
			return Long.compare(x, o2.x);
		}

		public double dist(Point p) {
			return Math.sqrt((x - p.x) * (x - p.x) + (y - p.y) * (y - p.y));
			//return Point._opSub(this, p).norm();
		}

		public long abs() {
			return (x * x) + (y * y);
		}

		public double norm() {
			return Math.sqrt(abs());
		}

		public static long _opMul(Point lhs, Point rhs) {

			return ((lhs.x * rhs.x) + (lhs.y * rhs.y));
		}

		public static long _opPow(Point lhs, Point rhs) {
			return ((lhs.x * rhs.y) - (lhs.y * rhs.x));
		}

		public static Point _opSub(Point lhs, Point rhs) {
			return new Point((lhs.x - rhs.x), (lhs.y - rhs.y));
		}

		public static Point _opPlus(Point lhs, Point rhs) {
			return new Point((lhs.x + rhs.x), (lhs.y + rhs.y));
		}


		public String toString() {
			return x + " " + y;
		}


		public int hashCode() {
			return Long.hashCode(x) ^ Long.hashCode(y);
		}

		public boolean equals(Object obj) {
			if (obj instanceof Point) {
				return compareTo((Point) obj) == 0;
			}
			return false;
		}

	}

	static class Line {
		Point a;
		Point ab;

		Line(Point a, Point b, boolean twoPoints) {
			this.a = new Point(a);
			if (twoPoints) {
				this.ab = Point._opSub(b, a);
			} else {
				this.ab = new Point(b);
			}
		}

		Line(long xa, long ya, long xb, long yb) {
			this.a = new Point(xa, ya);

			this.ab = new Point((xb - xa), (yb - ya));
		}

		Point b() {
			return Point._opPlus(a, ab);
		}

		public double distSegment(Point point) {
//        if (((point - se.a) * se.ab) <= 0) return dist(point, se.a);
//        if (((point - se.b()) * se.ab) >= 0) return dist(point, se.b());
//        return distLine(point, se);

			if (Point._opMul(Point._opSub(point, a), ab) <= 0) return point.dist(a);
			if (Point._opMul(Point._opSub(point, this.b()), ab) >= 0) return point.dist(this.b());
			return distLine(point);
		}


		public String toString() {
			return "Line{" +
					"(" + a +
					") (" + b() +
					")}";
		}

		public double distLine(Point point) {
			//if (!line) return dist(point, line.a);
			//return abs((point - line.a) ^ line.ab) / norm(line.ab);

			if (this.ab.isZeroPoint()) return a.dist(point);
			Point temp = Point._opSub(point, this.a);
			long temp2 = Point._opPow(temp, ab);

			return Math.abs(temp2) / this.ab.norm();
		}

		public static Line makeLine(Point p1, Point p2, boolean twoPoints) {
			return new Line(p1, p2, twoPoints);
		}

	}
}