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.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.io.Writer;
import java.io.InputStream;

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

class TaskE {
    public void solve(int testNumber, FastScanner in, FastPrinter out) {
        int n = in.nextInt();
        int h = in.nextInt();
        int f = in.nextInt();
        Line[] z = new Line[4 * n];
        for (int i = 0; i < n; i++) {
            int left = in.nextInt();
            int right = in.nextInt();
            z[4 * i] = new Line(true, new Point2DInteger(0, f), new Point2DInteger(left, h));
            z[4 * i + 1] = new Line(false, new Point2DInteger(0, f), new Point2DInteger(right, h));
            z[4 * i + 2] = new Line(true, new Point2DInteger(0, -f), new Point2DInteger(left, -h));
            z[4 * i + 3] = new Line(false, new Point2DInteger(0, -f), new Point2DInteger(right, -h));
        }
        int iter = 2000;
        Event[] s = new Event[4 * n];
        for (int i = 0; i < 4 * n; i++) {
            s[i] = new Event(0, false);
        }
        double answer = 0;
        for (int it = 0; it < iter; it++) {
            double y = 2. * h * it / iter - h;
            for (int i = 0; i < 4 * n; i++) {
                s[i].x = z[i].get(y);
                s[i].begin = z[i].begin;
            }
            Arrays.sort(s);
            double last = Double.NEGATIVE_INFINITY;
            double sum = 0;
            int count = 0;
            for (int i = 0; i < 4 * n; i++) {
                if (count > 0) {
                    sum += s[i].x - last;
                }
                if (s[i].begin) {
                    ++count;
                } else {
                    --count;
                }
                last = s[i].x;
            }
            answer += sum;
        }
        out.println(2 * h * answer / iter);
    }

    static class Event implements Comparable<Event> {
        double x;
        boolean begin;

        Event(double x, boolean begin) {
            this.x = x;
            this.begin = begin;
        }

        public int compareTo(Event o) {
            return Double.compare(x, o.x);
        }
    }

    static class Line {
        boolean begin;
        Point2DInteger p, q;

        Line(boolean begin, Point2DInteger p, Point2DInteger q) {
            this.begin = begin;
            this.p = p;
            this.q = q;
        }

        double get(double y) {
            return p.x + 1. * (q.x - p.x) / (q.y - p.y) * (y - p.y);
        }
    }
}

class FastScanner extends BufferedReader {

    boolean isEOF;

    public FastScanner(InputStream is) {
        super(new InputStreamReader(is));
    }

    public int read() {
        try {
            int ret = super.read();
            if (isEOF && ret < 0) {
                throw new InputMismatchException();
            }
            isEOF = ret == -1;
            return ret;
        } catch (IOException e) {
            throw new InputMismatchException();
        }
    }

    static boolean isWhiteSpace(int c) {
        return c >= -1 && c <= 32;
    }

    public int nextInt() {
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int ret = 0;
        while (!isWhiteSpace(c)) {
            if (c < '0' || c > '9') {
                throw new NumberFormatException("digit expected " + (char) c
                        + " found");
            }
            ret = ret * 10 + c - '0';
            c = read();
        }
        return ret * sgn;
    }

    }

class FastPrinter extends PrintWriter {

    public FastPrinter(OutputStream out) {
        super(out);
    }

    public FastPrinter(Writer out) {
        super(out);
    }


}

class Point2DInteger {
    public int x;
    public int y;

    public Point2DInteger(int x, int y) {
        this.x = x;
        this.y = y;
    }

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

    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Point2DInteger that = (Point2DInteger) o;

        if (x != that.x) return false;
        if (y != that.y) return false;

        return true;
    }

    public int hashCode() {
        int result = x;
        result = 31 * result + y;
        return result;
    }


    }