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;
vector<pair<int, int>> vec, vec1;
const double PI = acos(double(-1));
const double INF = 1e10;
const double EPS = 1e-8;
inline double sqr(double x) { return x * x; }
struct PT {
  double x, y;
  PT() {}
  PT(double x, double y) : x(x), y(y) {}
  void in() { scanf("%lf%lf", &x, &y); }
};
bool operator<(const PT &p1, const PT &p2) {
  if (fabs(p1.x - p2.x) > EPS) return p1.x < p2.x;
  return p1.y + EPS < p2.y;
}
bool operator==(const PT &p1, const PT &p2) {
  return fabs(p1.x - p2.x) < EPS && fabs(p1.y - p2.y) < EPS;
}
PT operator+(PT p1, PT p2) { return PT(p1.x + p2.x, p1.y + p2.y); }
PT operator-(PT p1, PT p2) { return PT(p1.x - p2.x, p1.y - p2.y); }
PT operator*(PT p, double c) { return PT(p.x * c, p.y * c); }
PT operator/(PT p, double c) { return PT(p.x / c, p.y / c); }
double dis(PT p) { return sqrt(sqr(p.x) + sqr(p.y)); }
double dis2(PT p) { return sqr(p.x) + sqr(p.y); }
double dis2(PT p1, PT p2) { return sqr(p1.x - p2.x) + sqr(p1.y - p2.y); }
double dis(PT p1, PT p2) { return sqrt(dis2(p1, p2)); }
double vect(PT p1, PT p2) { return p1.x * p2.y - p2.x * p1.y; }
double scal(PT p1, PT p2) { return p1.x * p2.x + p1.y * p2.y; }
double getAngle(PT p) { return atan2(p.y, p.x); }
double vect(PT p, PT p1, PT p2) { return vect(p1 - p, p2 - p); }
double scal(PT p, PT p1, PT p2) { return scal(p1 - p, p2 - p); }
double getAngle(PT p, PT p1, PT p2) {
  return getAngle(p2 - p) - getAngle(p1 - p);
}
double getAngle180(PT p, PT p1, PT p2) {
  return acos(scal(p, p1, p2) / dis(p, p1) / dis(p, p2));
}
double disToLine(PT p, PT p1, PT p2) {
  return fabs(vect(p, p1, p2)) / dis(p1, p2);
}
double disToSeg(PT p, PT p1, PT p2) {
  if (scal(p1, p, p2) < 0) return dis(p, p1);
  if (scal(p2, p, p1) < 0) return dis(p, p2);
  return disToLine(p, p1, p2);
}
bool onLine(PT p, PT p1, PT p2) { return fabs(vect(p1 - p, p2 - p)) < EPS; }
bool onSeg(PT p, PT p1, PT p2) {
  if (!onLine(p, p1, p2)) return 0;
  return (p1.x - p.x) * (p2.x - p.x) < EPS && (p1.y - p.y) * (p2.y - p.y) < EPS;
}
PT projection(PT a, PT b, PT p) {
  return a + (a - b) * (scal(p - a, a - b) / dis2(a - b));
}
int posLineLine(PT p1, PT p2, PT p3, PT p4, PT &p) {
  double s1 = vect(p1, p2, p3), s2 = vect(p1, p2, p4);
  if (fabs(s1 - s2) < EPS) {
    if (fabs(s1) < EPS) return 2;
    return 0;
  }
  p = p3 + (p4 - p3) * s1 / (s1 - s2);
  return 1;
}
int posCirLine(PT p, double r, PT p1, PT p2, PT *q) {
  double a, b, c, d2, d;
  a = dis2(p1, p2);
  b = scal(p1, p, p2);
  c = dis2(p, p1) - sqr(r);
  d2 = sqr(b) - a * c;
  if (d2 < -EPS) return 0;
  d = sqrt(fabs(d2));
  q[0] = p1 + (p2 - p1) * (b + d) / a;
  if (d2 < EPS) return 1;
  q[1] = p1 + (p2 - p1) * (b - d) / a;
  return 2;
}
int posCirCir(PT p1, double r1, PT p2, double r2, PT *q) {
  double dx, dy, d, e, f2, f;
  dx = p2.x - p1.x, dy = p2.y - p1.y;
  d = dis(p1, p2);
  e = (sqr(r1) - sqr(r2) + sqr(d)) / 2 / d;
  f2 = sqr(r1) - sqr(e);
  if (f2 < -EPS) return 0;
  f = sqrt(fabs(f2));
  q[0] = PT(p1.x + (e * dx - f * dy) / d, p1.y + (e * dy + f * dx) / d);
  if (f2 < EPS) return 1;
  q[1] = PT(p1.x + (e * dx + f * dy) / d, p1.y + (e * dy - f * dx) / d);
  return 2;
}
double calcArea(PT *p, int n) {
  double rlt = 0;
  for (int i = 0; i < n; i++) rlt += vect(p[i], p[(i + 1) % n]);
  return rlt / 2;
}
int inPolygon(PT p, PT *q, int m) {
  PT p1, p2;
  int k = 0;
  for (int i = 0; i < m; i++) {
    p1 = q[i], p2 = q[(i + 1) % m];
    if (onSeg(p, p1, p2)) return 2;
    if (p1.y > p2.y) swap(p1, p2);
    if (p1.y < p.y + EPS && p.y + EPS < p2.y && vect(p, p1, p2) > 0) k++;
  }
  return k % 2;
}
int convex_hull(PT *p, int n, PT *q) {
  sort(p, p + n);
  n = unique(p, p + n) - p;
  if (n == 1) {
    q[0] = p[0];
    return 1;
  }
  int m = 0;
  for (int i = 0; i < n; i++) {
    while (m > 1 && vect(q[m - 2], q[m - 1], p[i]) < EPS) m--;
    q[m++] = p[i];
  }
  int k = m;
  for (int i = n - 2; i >= 0; i--) {
    while (m > k && vect(q[m - 2], q[m - 1], p[i]) < EPS) m--;
    q[m++] = p[i];
  }
  return --m;
}
const int N = 1100;
PT R[N], S[N];
double inter(PT *p, int n, PT *q, int m) {
  int rn = 0;
  for (int i = 0; i < n; i++)
    if (inPolygon(p[i], q, m)) R[rn++] = p[i];
  for (int i = 0; i < m; i++)
    if (inPolygon(q[i], p, n)) R[rn++] = q[i];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      PT tmp;
      int ret = posLineLine(p[i], p[(i + 1) % n], q[j], q[(j + 1) % m], tmp);
      if (ret == 1 && onSeg(tmp, p[i], p[(i + 1) % n]) &&
          onSeg(tmp, q[j], q[(j + 1) % m])) {
        R[rn++] = tmp;
      }
    }
  }
  int sn = convex_hull(R, rn, S);
  return fabs(calcArea(S, sn));
}
int main() {
  int n, h, f;
  scanf("%d%d%d", &n, &h, &f);
  for (int i = 0; i < n; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    vec.emplace_back(l, r);
  }
  sort(vec.begin(), vec.end());
  int la = -1111111;
  for (int i = 0; i < vec.size(); ++i) {
    int l = vec[i].first, r = vec[i].second;
    if (l > la)
      vec1.emplace_back(l, r);
    else {
      auto t = vec1.back();
      vec1.pop_back();
      vec1.emplace_back(t.first, max(r, t.second));
    }
  }
  vec = vec1;
  double area = 0;
  for (auto &t : vec) {
    int l = t.first, r = t.second;
    PT p[4] = {PT(l, h), PT(r, h), PT(1.0 * r * (h + f) / (f - h), -h),
               PT(1.0 * l * (h + f) / (f - h), -h)};
    area += 2.0 * fabs(calcArea(p, 4));
    for (auto &s : vec) {
      int _l = s.first, _r = s.second;
      PT q[4] = {PT(_l, -h), PT(_r, -h), PT(1.0 * _r * (h + f) / (f - h), h),
                 PT(1.0 * _l * (h + f) / (f - h), h)};
      area -= inter(p, 4, q, 4);
    }
  }
  printf("%.10lf\n", area);
  return 0;
}