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.util.*;
import java.io.*;

public class Solution {
    int n, h, f;
    
    class Window {
        double l, r;
        public Window(double l, double r) {
            if (l == 0.0)
                l = 1e-9;
            
            this.l = l;
            this.r = r;
        }
    }
    
    class Line {
        double x1, y1, x2, y2;
        double A, B, C;
        
        public Line(double x1, double y1, double x2, double y2) {
            this.x1 = x1;
            this.y1 = y1;
            this.x2 = x2;
            this.y2 = y2;
            
            this.A = y2 - y1;
            this.B = x1 - x2;
            this.C = -A * x1 - B * y1;
        }
    }
    
    class Point {
        double x, y;
        public Point(double x, double y) {
            this.x = x;
            this.y = y;
        }
    }
    
    Point intr(Line l1, Line l2) {
        return new Point((l2.C * l1.B - l1.C * l2.B) / (l1.A * l2.B - l2.A * l1.B),
                (l2.C * l1.A - l1.C * l2.A) / (l1.B * l2.A - l2.B * l1.A));
    }
        
    double area(Point[] pnt) {
        double res = 0;
        int n = pnt.length;
        for (int i=0; i < n; i++) {
            int ii = i == n - 1 ? 0 : i + 1;
            res += (pnt[ii].x - pnt[i].x) * (pnt[ii].y + pnt[i].y);
        }
        return Math.abs(res) / 2.0;
    }
    
    
    double areaAbove(Point[] pp, double h) {
        int n = pp.length;
        Point[] pnt = new Point[n];
        for (int i=0; i < n; i++)
            pnt[i] = new Point(pp[i].x, pp[i].y - h);
        
        double res = 0;
        for (int i=0; i < n; i++) {
            int ii = i == n - 1 ? 0 : i + 1;
            
            if (pnt[i].y >= 0 && pnt[ii].y >= 0) {
                res += (pnt[ii].x - pnt[i].x) * (pnt[ii].y + pnt[i].y);
            } else if (pnt[i].y < 0 && pnt[ii].y >= 0) {
                Point mid = intr(new Line(pnt[i].x, pnt[i].y, pnt[ii].x, pnt[ii].y),
                        new Line(0, 0, 1, 0));
                res += (pnt[ii].x - mid.x) * (pnt[ii].y + mid.y);
            } else if (pnt[i].y >= 0 && pnt[ii].y < 0) {
                Point mid = intr(new Line(pnt[i].x, pnt[i].y, pnt[ii].x, pnt[ii].y),
                        new Line(0, 0, 1, 0));
                res += (mid.x - pnt[i].x) * (mid.y + pnt[i].y); 
            }
        }
        return Math.abs(res) / 2.0;
    }

    
    double solve(List<Window> wins) {
        double res = 0.0;
        
        int n = wins.size();
        
        Line top = new Line(-1, h, 1, h);
        
        List<Window> opp = new ArrayList<Window>();
        
        for (int i=0; i < n; i++) {
            opp.add(new Window(intr(top, new Line(0, -f, wins.get(i).l, -h)).x,
                    intr(top, new Line(0, -f, wins.get(i).r, -h)).x));
        }
        
        for (int i=0; i < n; i++) {
            res += 2 * area(new Point[] {
                new Point(wins.get(i).l, -h),
                new Point(opp.get(i).l, h),
                new Point(opp.get(i).r, h),
                new Point(wins.get(i).r, -h)
            });
        }
        
        for (int i=0; i < n; i++)
            for (int j=0; j < n; j++) {
                Line li_left = new Line(wins.get(i).l, -h, opp.get(i).l, h);
                Line li_right = new Line(wins.get(i).r, -h, opp.get(i).r, h);
                
                Line lj_left = new Line(wins.get(j).l, h, opp.get(j).l, -h);
                Line lj_right = new Line(wins.get(j).r, h, opp.get(j).r, -h);
                
                Point[] pnt = new Point[] {
                    intr(li_left, lj_left),
                    intr(li_left, lj_right),
                    intr(li_right, lj_right),
                    intr(li_right, lj_left)
                };
                
                double intrArea = areaAbove(pnt, -h) - areaAbove(pnt, h);
                
                res -= intrArea;
            }
        
        return res;
    }
    
    public void go() throws Exception {
        Scanner sc = new Scanner(new InputStreamReader(System.in));
        n = sc.nextInt();
        h = sc.nextInt();
        f = sc.nextInt();
        List<Window> pos = new ArrayList<Window>();
        List<Window> neg = new ArrayList<Window>();
        for (int i=0; i < n; i++) {
            int l = sc.nextInt();
            int r = sc.nextInt();
            if (l >= 0 && r >= 0) {
                pos.add(new Window(l, r));
            } else if (l <= 0 && r <= 0) {
                neg.add(new Window(-r, -l));
            } else {
                pos.add(new Window(0, r));
                neg.add(new Window(0, -l));
            }
        }
        sc.close();
        
        System.out.println(solve(pos) + solve(neg));
    }
    
    public static void main(String[] args) throws Exception {
        (new Solution()).go();
    }
}