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>
#pragma comment(linker, "/STACK:102400000,102400000")
template <class T>
inline void gmax(T &a, T b) {
  if (b > a) a = b;
}
template <class T>
inline void gmin(T &a, T b) {
  if (b < a) a = b;
}
using namespace std;
const int N = 1000 + 10, M = 2e6 + 10, Z = 1e9 + 7, maxint = 2147483647,
          ms1 = 16843009, ms31 = 522133279, ms63 = 1061109567,
          ms127 = 2139062143;
const double PI = acos(-1.0), eps1 = 1e-8;
void fre() {
  freopen("/Users/luras/Desktop/in.txt", "r", stdin);
  freopen("/Users/luras/Desktop/out.txt", "w", stdout);
}
const int INF = 1e9;
int casenum, casei;
const double eps = 1e-12, inf = 1e18;
inline double sqr(double x) { return x * x; }
inline int sgn(double x) { return x < -eps ? -1 : (x > eps); }
inline double fix(double x) { return sgn(x) == 0 ? 0 : x; }
struct point {
  double x, y;
  point(double x = 0, double y = 0) : x(x), y(y) {}
  bool operator<(const point &rhs) const {
    return sgn(x - rhs.x) < 0 || (sgn(x - rhs.x) == 0 && sgn(y - rhs.y) < 0);
  }
  bool operator==(const point &rhs) const {
    return sgn(x - rhs.x) == 0 && sgn(y - rhs.y) == 0;
  }
  point operator+(const point &rhs) const {
    return point(x + rhs.x, y + rhs.y);
  }
  point operator-(const point &rhs) const {
    return point(x - rhs.x, y - rhs.y);
  }
  point operator*(const double k) const { return point(x * k, y * k); }
  point operator/(const double k) const { return point(x / k, y / k); }
  double dot(const point &rhs) const { return x * rhs.x + y * rhs.y; }
  double det(const point &rhs) const { return x * rhs.y - y * rhs.x; }
  double norm2() const { return x * x + y * y; }
  double norm() const { return hypot(x, y); }
};
std::vector<point> polygon[N];
std::vector<point> convex_hull(std::vector<point> u) {
  std::sort(u.begin(), u.end());
  u.erase(std::unique(u.begin(), u.end()), u.end());
  if (u.size() < 3u) return u;
  std::vector<point> ret;
  for (size_t i = 0, o = 1, m = 1; ~i; i += o) {
    while (ret.size() > m) {
      point A = ret.back() - ret[ret.size() - 2];
      point B = ret.back() - u[i];
      if (sgn(A.det(B)) < 0) break;
      ret.pop_back();
    }
    ret.push_back(u[i]);
    if (i + 1 == u.size()) m = ret.size(), o = -1;
  }
  ret.pop_back();
  return ret;
}
inline double rati(const point &A, const point &B, const point &O) {
  if (sgn(A.x - B.x) == 0)
    return (O.y - A.y) / (B.y - A.y);
  else
    return (O.x - A.x) / (B.x - A.x);
}
double polygon_union(std::vector<point> poly[], int n) {
  double ret = 0;
  for (int i = 0; i < n; ++i) {
    for (size_t v = 0; v < poly[i].size(); ++v) {
      point A = poly[i][v], B = poly[i][(v + 1) % poly[i].size()];
      std::vector<std::pair<double, int> > segs;
      segs.push_back(std::make_pair(0.0, 0));
      segs.push_back(std::make_pair(1.0, 0));
      for (int j = 0; j < n; ++j)
        if (i != j) {
          for (size_t u = 0; u < poly[j].size(); ++u) {
            point C = poly[j][u], D = poly[j][(u + 1) % poly[j].size()];
            int sc = sgn((B - A).det(C - A)), sd = sgn((B - A).det(D - A));
            if (sc == 0 && sd == 0) {
              if (sgn((B - A).dot(D - C)) > 0 && i > j) {
                segs.push_back(std::make_pair(rati(A, B, C), +1));
                segs.push_back(std::make_pair(rati(A, B, D), -1));
              }
            } else {
              double sa = (D - C).det(A - C), sb = (D - C).det(B - C);
              if (sc >= 0 && sd < 0)
                segs.push_back(std::make_pair(sa / (sa - sb), 1));
              else if (sc < 0 && sd >= 0)
                segs.push_back(std::make_pair(sa / (sa - sb), -1));
            }
          }
        }
      std::sort(segs.begin(), segs.end());
      double pre = std::min(std::max(segs[0].first, 0.0), 1.0), now, sum = 0;
      int cnt = segs[0].second;
      for (size_t j = 1; j < segs.size(); ++j) {
        now = std::min(std::max(segs[j].first, 0.0), 1.0);
        if (!cnt) sum += now - pre;
        cnt += segs[j].second;
        pre = now;
      }
      ret += A.det(B) * sum;
    }
  }
  return ret / 2;
}
int n;
double h, f;
void run() {
  double x, y, th, ret = 0;
  int t = 0;
  for (int i = 0; i < n; ++i) {
    double l, r;
    scanf("%lf%lf", &l, &r);
    point rect[4];
    rect[0].x = l, rect[0].y = -h;
    rect[1].x = r, rect[1].y = -h;
    rect[2].x = r * (h + f) / (-h + f), rect[2].y = h;
    rect[3].x = l * (h + f) / (-h + f), rect[3].y = h;
    polygon[t].clear();
    for (int j = 0; j < 4; ++j) {
      polygon[t].push_back(rect[j]);
    }
    polygon[t] = convex_hull(polygon[t]);
    t++;
    rect[0].x = r, rect[0].y = h;
    rect[1].x = l, rect[1].y = h;
    rect[2].x = l * (-h - f) / (h - f), rect[2].y = -h;
    rect[3].x = r * (-h - f) / (h - f), rect[3].y = -h;
    polygon[t].clear();
    for (int j = 0; j < 4; ++j) {
      polygon[t].push_back(rect[j]);
    }
    polygon[t] = convex_hull(polygon[t]);
    t++;
  }
  ret += polygon_union(polygon, t);
  printf("%.10f\n", ret);
}
int main() {
  while (~scanf("%d%lf%lf", &n, &h, &f)) {
    run();
  }
  return 0;
}