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:
//package yandex2011.q2;
import java.awt.geom.Line2D;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class E {
	Scanner in;
	PrintWriter out;
//	String INPUT = "2 2 4\r\n" +
//			"-1 0 1 2";
//	String INPUT = "2 2 4\r\n" +
//			"-1 0\r\n" +
//			"1 2";
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		double h = ni();
		double f = ni();
		double[] l = new double[n];
		double[] r = new double[n];
		for(int i = 0;i < n;i++){
			l[i] = ni();
			r[i] = ni();
		}
		
		double S = 0;
		for(int i = 0;i < n;i++){
			S += 2.0*f*(r[i] - l[i])*h/(f-h)*2;
		}
		
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				double dl = (f+h)/(f-h)*l[i];
				double dr = (f+h)/(f-h)*r[i];
				double ul = (f+h)/(f-h)*l[j];
				double ur = (f+h)/(f-h)*r[j];
				double[][] ip = interPoly(
						new double[]{l[i], dl, dr, r[i]},
						new double[]{h, -h, -h, h},
						new double[]{ul, l[j], r[j], ur},
						new double[]{h, -h, -h, h}
						);
				if(ip[0].length > 0){
					S -= areaPoly(ip[0], ip[1]);
				}
			}
		}
		out.println(S);
	}
	
	public static double areaPoly(double[] x, double[] y)
	{
		int n = x.length;
		double s = 0;
		for(int i = 0;i < n - 1;i++){
			s += (x[i]*y[i+1]-x[i+1]*y[i]) / 2;
		}
		s += (x[n-1]*y[0]-x[0]*y[n-1]) / 2;
		return Math.abs(s);
	}
	
	public boolean isOnIn(double x, double y, double[] px, double[] py)
	{
		int n = px.length;
		int cc = Line2D.relativeCCW(px[n-1], py[n-1], px[0], py[0], x, y);
		if(cc == 0)return true;
		for(int i = 0;i < n-1;i++){
			int ccc = Line2D.relativeCCW(px[i], py[i], px[i+1], py[i+1], x, y);
			if(ccc == 0)return true;
			if(cc != ccc)return false;
		}
		return true;
	}
	
	public void convexSort(double[] sx, double[] sy)
	{
		double gx = 0, gy = 0;
		for(double x : sx)gx += x;
		for(double y : sy)gy += y;
		int n = sx.length;
		gx /= n; gy /= n;
		
		final double[] th = new double[n];
		for(int i = 0;i < n;i++){
			th[i] = Math.atan2(sy[i]-gy, sx[i]-gx);
		}
		Integer[] ord = new Integer[n];
		for(int i = 0;i < n;i++)ord[i] = i;
		Arrays.sort(ord, new Comparator<Integer>(){
			public int compare(Integer a, Integer b){
				return (int)Math.signum(th[a] - th[b]);
			}
		});
		
		double[] cx = new double[n];
		double[] cy = new double[n];
		System.arraycopy(sx, 0, cx, 0, n);
		System.arraycopy(sy, 0, cy, 0, n);
		for(int i = 0;i < n;i++){
			sx[i] = cx[ord[i]];
			sy[i] = cy[ord[i]];
		}
	}
	
	public double[][] interPoly(double[] x1, double[] y1, double[] x2, double[] y2)
	{
		int m = x1.length;
		int n = x2.length;
		double[] cx = new double[2*(m+n)];
		double[] cy = new double[2*(m+n)];
		int p = 0;
		for(int i = 0;i < m;i++){
			for(int j = 0;j < n;j++){
				int ni = (i+1)%m;
				int nj = (j+1)%n;
				double[] il = interLines(x1[i], y1[i], x1[ni], y1[ni], x2[j], y2[j], x2[nj], y2[nj]);
				if(il != null && il[2] > -EPS && il[2] < 1+EPS && il[3] > -EPS && il[3] < 1+EPS){
					cx[p] = il[0];
					cy[p] = il[1];
					p++;
				}
			}
		}
		for(int i = 0;i < m;i++){
			if(isOnIn(x1[i], y1[i], x2, y2)){
				cx[p] = x1[i];
				cy[p] = y1[i];
				p++;
			}
		}
		for(int i = 0;i < n;i++){
			if(isOnIn(x2[i], y2[i], x1, y1)){
				cx[p] = x2[i];
				cy[p] = y2[i];
				p++;
			}
		}
		
		cx = Arrays.copyOf(cx, p);
		cy = Arrays.copyOf(cy, p);
		
		convexSort(cx, cy);
		
		return new double[][]{cx, cy};
	}
	
	static double EPS = 1E-9;
	
	public static double[] interLines(double ax, double ay, double bx, double by, double cx, double cy, double dx, double dy)
	{
		double aa = bx - ax;
		double cc = by - ay;
		double bb = cx - dx;
		double dd = cy - dy;
		double xx = cx - ax;
		double yy = cy - ay;
		double det = aa * dd - bb * cc;
		if(Math.abs(det) < EPS)return null;
		double t = (dd * xx - bb * yy) / det;
		double u = (-cc * xx + aa * yy) / det;
		return new double[]{ax + (bx - ax) * t, ay + (by - ay) * t, t, u};
	}
	
	void run() throws Exception
	{
		in = INPUT.isEmpty() ? new Scanner(System.in) : new Scanner(INPUT);
		out = new PrintWriter(System.out);

		solve();
		out.flush();
	}
	
	
	public static void main(String[] args) throws Exception
	{
		new E().run();
	}
	
	int ni() { return Integer.parseInt(in.next()); }
	double nd() { return Double.parseDouble(in.next()); }
	void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}