Problem: Consider a house plan. 

Let the house be represented by an infinite horizontal strip defined by the inequality  - h ≤ y ≤ h. Strictly outside the house there are two light sources at the points (0, f) and (0, - f). Windows are located in the walls, the windows are represented by segments on the lines y = h and y = - h. Also, the windows are arranged symmetrically about the line y = 0.

Your task is to find the area of the floor at the home, which will be lighted by the sources of light. 

<image>

Input

The first line of the input file contains three integers n, h and f (1 ≤ n ≤ 500, 1 ≤ h ≤ 10, h < f ≤ 1000). Next, n lines contain two integers each li, ri ( - 5000 ≤ li < ri ≤ 5000), each entry indicates two segments. Endpoints of the first segment are (li, h)-(ri, h), and endpoints of the second segment are (li, - h)-(ri, - h). These segments describe location of windows. Numbers in the lines are space-separated. It is guaranteed that no two distinct segments have common points. 

Output

Print the single real number — the area of the illuminated part of the floor with an absolute or relative error of no more than 10 - 4.

Examples

Input

1 1 2
-1 1


Output

10.0000000000


Input

2 2 4
-1 0
1 2


Output

23.3333333333

Note

The second sample test is shown on the figure. Green area is the desired area of the illuminated part of the floor. Violet segments indicate windows.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main implements Runnable {
	
	final static double eps = 1e-8;
	
	class Point {
		double x, y;
		Point(double x, double y) {
			this.x = x;
			this.y = y;
		}
		Point sub(Point o) {
			return new Point(x - o.x, y - o.y);
		}
		Point add(Point o) {
			return new Point(x + o.x, y + o.y);
		}
		Point scale(double f) {
			return new Point(f * x, f * y);
		}
		@Override
		public String toString() {
			return String.format("(%.2f %.2f)", x, y);
		}
	}
	
	double dot(Point a, Point b) {
		return a.x * b.x + a.y * b.y;
	}
	
	double cross(Point a, Point b) {
		return a.x * b.y - a.y * b.x;
	}
	
	class Triangle {
		Point a, b, c;
		Triangle(Point a, Point b, Point c) {
			this.a = a;
			this.b = b;
			this.c = c;
		}
		List<Point> toPolygon() {
			List<Point> res = new ArrayList<Point>();
			res.add(a);
			res.add(b);
			res.add(c);
			return res;
		}
		@Override
		public String toString() {
			return toPolygon().toString();
		}
	}

	public void _main() throws IOException {
		int n = nextInt();
		h = nextDouble();
		f = nextDouble();
		double[] l = new double[n];
		double[] r = new double[n];
		Triangle[] tr1 = new Triangle[n];
		Triangle[] tr2 = new Triangle[n];
		for (int i = 0; i < n; i++) {
			l[i] = nextDouble();
			r[i] = nextDouble();
			tr1[i] = getTriangle(l[i], r[i], true);
			tr2[i] = getTriangle(l[i], r[i], false);
		}
		double sum = 0;
		for (int i = 0; i < n; i++) {
			Point a = new Point(1e5, h);
			Point b = new Point(-1e5, h);
			List<Point> pp = tr1[i].toPolygon();
			sum += area(cut(pp, a, b));
		}
		sum *= 2;
		double intersection = 0;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				//if (i == j) continue;				
				double f = intersectTriangles(tr1[i].a, tr1[i].b, tr1[i].c, tr2[j].a, tr2[j].b, tr2[j].c);
				if (!Double.isNaN(f)) {
					intersection += f;
				}
				else {
					out.println(i + " " + j);
				}
			}
		}
		//out.println(sum + " " + intersection);
		out.printf("%.4f\n", sum - intersection);
	}
	
	private Triangle getTriangle(double l, double r, boolean up) {
		Point a, b, c;
		if (up) {
			a = new Point(0, f);
			b = new Point(l, h);
			c = new Point(r, h);			
		}
		else {
			a = new Point(0, -f);
			b = new Point(l, -h);
			c = new Point(r, -h);
		}
		b = a.add((b.sub(a)).scale((f + h)  / (f - h)));
		c = a.add((c.sub(a)).scale((f + h)  / (f - h)));
		return new Triangle(a, b, c);
	}

	double h, f;


	private double intersectTriangles(Point a, Point b, Point c, Point m, Point n, Point k) {
		List<Point> poly = new ArrayList<Point>();
		if (cross(b.sub(a), c.sub(a)) < 0) {
			Point t = b;
			b = c;
			c = t;
		}
		if (cross(n.sub(m), k.sub(m)) < 0) {
			Point t = n;
			n = k;
			k = t;
		}
		poly.add(a);
		poly.add(b);
		poly.add(c);
		poly = cut(poly, m, n);
		poly = cut(poly, n, k);
		poly = cut(poly, k, m);
		return area(poly);
	}

	private double area(List<Point> p) {
		int n = p.size();
		double res = 0;
		for (int i = 0; i < n; i++) {
			int j = (i + 1) % n;
			double dx = p.get(j).x - p.get(i).x;
			double sy = p.get(j).y + p.get(i).y;
			res += dx * sy;
		}
		return 0.5 * Math.abs(res);
	}


	private List<Point> cut(List<Point> p, Point a, Point b) {
		List<Point> res = new ArrayList<Point>();
		for (int i = 0; i < p.size(); i++) {
			Point pi = p.get(i);
			Point pj = p.get((i + 1) % p.size());
			int si = side(pi, a, b);
			int sj = side(pj, a, b);
			if (si > 0 && sj > 0) continue;
			if (si == 0 || (si < 0 && sj < 0)) {
				res.add(pi);
				continue;
			}
			double d1 = cross(a.sub(pi), pj.sub(pi));
			double d2 = cross(b.sub(pi), pj.sub(pi));
			if (Math.abs(d1 - d2) < eps) throw new AssertionError();
			double xk = (b.x * d1 - a.x * d2) / (d1 - d2);
			double yk = (b.y * d1 - a.y * d2) / (d1 - d2);			
			Point pk = new Point(xk, yk);
			if (si < 0) {
				res.add(pi);
				res.add(pk);
			}
			else {
				res.add(pk);
				res.add(pj);
			}
		}
		if (res.isEmpty())
			return res;
		for (int i = res.size() - 1; i >= 0; i--) {
			int j = (i + 1) % res.size();
			double dx = res.get(i).x - res.get(j).x;
			double dy = res.get(i).y - res.get(j).y;
			if (Math.abs(dx) + Math.abs(dy) < eps) {
				res.remove(i);
			}
		}
		return res;
	}

	private int side(Point x, Point a, Point b) {
		double cr = cross(x.sub(a), b.sub(a));
		if (Math.abs(cr) < eps)
			return 0;
		return cr < 0 ? -1 : 1;
	}


	private BufferedReader in;
	private PrintWriter out;
	private StringTokenizer st;

	private String next() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String rl = in.readLine();
			if (rl == null)
				return null;
			st = new StringTokenizer(rl);
		}
		return st.nextToken();
	}

	private int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	private long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	private double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	public static void main(String[] args) {
		Locale.setDefault(Locale.UK);
		new Thread(new Main()).start();
	}

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);

			_main();

			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(202);
		}
	}

}