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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
struct point {
  double x, y;
  point() {}
  point(double a, double b) : x(a), y(b) {}
  void out() { cout << x << " " << y << endl; }
};
struct Line {
  point p1, p2;
  Line() {}
  Line(point a, point b) : p1(a), p2(b) {}
  bool operator<(const Line &b) const { return p1.x < b.p1.x; }
} line[600], line2[600];
struct Poly {
  point p[5];
} poly[600];
double xmult(point p1, point p2, point p0) {
  return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y);
}
double dmult(point p1, point p2, point p0) {
  return (p1.x - p0.x) * (p2.x - p0.x) + (p1.y - p0.y) * (p2.y - p0.y);
}
double distan(point p1, point p2) {
  return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
}
int dots_inline(point p1, point p2, point p3) {
  return (((xmult(p1, p2, p3)) > 0 ? (xmult(p1, p2, p3))
                                   : -(xmult(p1, p2, p3))) < 1e-8);
}
int dot_online_in(point p, point l1, point l2) {
  return (((xmult(p, l1, l2)) > 0 ? (xmult(p, l1, l2)) : -(xmult(p, l1, l2))) <
          1e-8) &&
         (l1.x - p.x) * (l2.x - p.x) < 1e-8 &&
         (l1.y - p.y) * (l2.y - p.y) < 1e-8;
}
int dot_online_ex(point p, point l1, point l2) {
  return dot_online_in(p, l1, l2) &&
         (!(((p.x - l1.x) > 0 ? (p.x - l1.x) : -(p.x - l1.x)) < 1e-8) ||
          !(((p.y - l1.y) > 0 ? (p.y - l1.y) : -(p.y - l1.y)) < 1e-8)) &&
         (!(((p.x - l2.x) > 0 ? (p.x - l2.x) : -(p.x - l2.x)) < 1e-8) ||
          !(((p.y - l2.y) > 0 ? (p.y - l2.y) : -(p.y - l2.y)) < 1e-8));
}
int same_side(point p1, point p2, point l1, point l2) {
  return xmult(l1, p1, l2) * xmult(l1, p2, l2) > 1e-8;
}
int opposite_side(point p1, point p2, point l1, point l2) {
  return xmult(l1, p1, l2) * xmult(l1, p2, l2) < -1e-8;
}
int parallel(point u1, point u2, point v1, point v2) {
  return ((((u1.x - u2.x) * (v1.y - v2.y) - (v1.x - v2.x) * (u1.y - u2.y)) > 0
               ? ((u1.x - u2.x) * (v1.y - v2.y) - (v1.x - v2.x) * (u1.y - u2.y))
               : -((u1.x - u2.x) * (v1.y - v2.y) -
                   (v1.x - v2.x) * (u1.y - u2.y))) < 1e-8);
}
int perpendicular(point u1, point u2, point v1, point v2) {
  return ((((u1.x - u2.x) * (v1.x - v2.x) + (u1.y - u2.y) * (v1.y - v2.y)) > 0
               ? ((u1.x - u2.x) * (v1.x - v2.x) + (u1.y - u2.y) * (v1.y - v2.y))
               : -((u1.x - u2.x) * (v1.x - v2.x) +
                   (u1.y - u2.y) * (v1.y - v2.y))) < 1e-8);
}
int intersect(point u1, point u2, point v1, point v2) {
  if (opposite_side(u1, u2, v1, v2) && opposite_side(v1, v2, u1, u2)) return 1;
  if (!dots_inline(u1, u2, v1) || !dots_inline(u1, u2, v2))
    if (!same_side(u1, u2, v1, v2) && !same_side(v1, v2, u1, u2)) return 2;
  if (dot_online_in(u1, v1, v2) || dot_online_in(u2, v1, v2) ||
      dot_online_in(v1, u1, u2) || dot_online_in(v2, u1, u2))
    return 3;
  return 0;
}
point intersection(point u1, point u2, point v1, point v2) {
  point ret = u1;
  double t = ((u1.x - v1.x) * (v1.y - v2.y) - (u1.y - v1.y) * (v1.x - v2.x)) /
             ((u1.x - u2.x) * (v1.y - v2.y) - (u1.y - u2.y) * (v1.x - v2.x));
  ret.x += (u2.x - u1.x) * t;
  ret.y += (u2.y - u1.y) * t;
  return ret;
}
double cut(Line L1, Line L2, int pos) {
  point ret[20], tp[20];
  for (int i = 0; i <= 4; i++) {
    ret[i] = poly[pos].p[i];
  }
  int size = 4;
  int cnt = -1;
  for (int i = 0; i < size; i++) {
    if (xmult(ret[i], L1.p2, L1.p1) > -1e-8) {
      ++cnt;
      tp[cnt] = ret[i];
    }
    if (xmult(ret[i], L1.p2, L1.p1) * xmult(ret[i + 1], L1.p2, L1.p1) < -1e-8) {
      point rr = intersection(L1.p1, L1.p2, ret[i], ret[i + 1]);
      cnt++;
      tp[cnt] = rr;
    }
  }
  cnt++;
  tp[cnt] = tp[0];
  size = cnt;
  for (int i = 0; i <= cnt; i++) ret[i] = tp[i];
  cnt = -1;
  for (int i = 0; i < size; i++) {
    if (xmult(ret[i], L2.p2, L2.p1) < 1e-8) {
      ++cnt;
      tp[cnt] = ret[i];
    }
    if (xmult(ret[i], L2.p2, L2.p1) * xmult(ret[i + 1], L2.p2, L2.p1) < -1e-8) {
      point rr = intersection(L2.p1, L2.p2, ret[i], ret[i + 1]);
      cnt++;
      tp[cnt] = rr;
    }
  }
  cnt++;
  tp[cnt] = tp[0];
  double are = 0.0;
  for (int i = 0; i < cnt; i++) {
    are += (tp[i].x * tp[i + 1].y - tp[i].y * tp[i + 1].x);
  }
  return fabs(are) / 2.0;
}
int main() {
  int n;
  double h, f;
  double ans = 0.0;
  scanf("%d", &n);
  scanf("%lf %lf", &h, &f);
  for (int i = 1; i <= n; i++) {
    scanf("%lf %lf", &line[i].p1.x, &line[i].p2.x);
    line[i].p1.y = line[i].p2.y = h;
    line2[i].p1.x = f * line[i].p1.x / (f - h);
    line2[i].p2.x = f * line[i].p2.x / (f - h);
    line2[i].p1.y = line2[i].p2.y = 0;
    ans +=
        (line[i].p2.x - line[i].p1.x + line2[i].p2.x - line2[i].p1.x) * h / 2.0;
  }
  sort(line + 1, line + n + 1);
  sort(line2 + 1, line2 + n + 1);
  double inf = 1e50;
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    if (i == 1) {
      ++cnt;
      poly[cnt].p[0] = point(-inf, 0);
      poly[cnt].p[1] = line2[i].p1;
      poly[cnt].p[2] = line[i].p1;
      poly[cnt].p[3] = point(-inf, h);
      poly[cnt].p[4] = poly[cnt].p[0];
    } else {
      ++cnt;
      poly[cnt].p[0] = line2[i - 1].p2;
      poly[cnt].p[1] = line2[i].p1;
      poly[cnt].p[2] = line[i].p1;
      poly[cnt].p[3] = line[i - 1].p2;
      poly[cnt].p[4] = poly[cnt].p[0];
    }
  }
  ++cnt;
  poly[cnt].p[0] = line2[n].p2;
  poly[cnt].p[1] = point(inf, 0);
  poly[cnt].p[2] = point(inf, h);
  poly[cnt].p[3] = line[n].p2;
  poly[cnt].p[4] = poly[cnt].p[0];
  for (int i = 1; i <= n; i++) {
    Line left, right;
    left.p1 = point(line[i].p1.x, -h);
    left.p2 = point(line2[i].p1.x, 0);
    right.p1 = point(line[i].p2.x, -h);
    right.p2 = point(line2[i].p2.x, 0);
    for (int j = 1; j <= cnt; j++) {
      if (xmult(poly[j].p[0], right.p2, right.p1) > -1e-8 &&
          xmult(poly[j].p[3], right.p2, right.p1) > -1e-8) {
        continue;
      }
      if (xmult(left.p2, poly[j].p[1], left.p1) > -1e-8 &&
          xmult(left.p2, poly[j].p[2], left.p1) > -1e-8) {
        continue;
      }
      ans += cut(left, right, j);
    }
  }
  ans = ans * 2.0;
  printf("%.8lf\n", ans);
}