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:64000000")
using namespace std;
template <typename first>
inline first abs(const first& a) {
  return a < 0 ? -a : a;
}
template <typename first>
inline first sqr(const first& a) {
  return a * a;
}
const long double PI = 3.1415926535897932384626433832795;
const long double EPS = 1e-9;
const int INF = 1000 * 1000 * 1000;
struct pt {
  long double x, y;
  pt(long double x = 0.0, long double y = 0.0) : x(x), y(y) {}
};
const int N = 500 + 13;
int n, h, f;
int lf[N], rg[N];
pt focus, mfocus;
pt lftop, rgtop, lfbot, rgbot;
inline long double det(const long double& ax, const long double& ay,
                       const long double& bx, const long double& by) {
  return ax * by - ay * bx;
}
inline bool between(const pt& c, const pt& a, const pt& b) {
  if (c.x + EPS < min(a.x, b.x) || c.x > max(a.x, b.x) + EPS) return false;
  if (c.y + EPS < min(a.y, b.y) || c.y > max(a.y, b.y) + EPS) return false;
  return true;
}
inline bool intersect(const pt& a, const pt& b, const pt& c, const pt& d, pt& p,
                      bool segm) {
  long double A1 = b.y - a.y, B1 = a.x - b.x, C1 = -(a.x * A1 + a.y * B1);
  long double A2 = d.y - c.y, B2 = c.x - d.x, C2 = -(c.x * A2 + c.y * B2);
  long double Det = det(A1, B1, A2, B2);
  if (abs(Det) < EPS) return false;
  p.x = det(-C1, B1, -C2, B2) / Det;
  p.y = det(A1, -C1, A2, -C2) / Det;
  if (segm) return between(p, a, b) && between(p, c, d);
  return true;
}
inline long double square(const vector<pt>& pol) {
  long double res = 0.0;
  for (int i = 0; i < int(int((pol).size())); i++) {
    int nexti = (i + 1 == int((pol).size()) ? 0 : i + 1);
    res += (pol[nexti].x - pol[i].x) * (pol[nexti].y + pol[i].y);
  }
  return abs(res) * 0.5;
}
inline int sign(const long double& c) {
  return c > EPS ? 1 : c < -EPS ? -1 : 0;
}
void cut(vector<pt>& pol, pt a, pt b, const pt& c) {
  if (int((pol).size()) < 3) return;
  long double A = b.y - a.y, B = a.x - b.x, C = -(a.x * A + a.y * B);
  int s = sign(A * c.x + B * c.y + C);
  pt v = pt((b.x - a.x) * 1e6, (b.y - a.y) * 1e6);
  a = pt(a.x - v.x, a.y - v.y);
  b = pt(b.x + v.x, b.y + v.y);
  vector<pt> ans;
  for (int i = 0; i < int(int((pol).size())); i++) {
    int nexti = (i + 1 == int((pol).size()) ? 0 : i + 1);
    int s1 = sign(A * pol[i].x + B * pol[i].y + C) * s;
    int s2 = sign(A * pol[nexti].x + B * pol[nexti].y + C) * s;
    if ((s1 < 0 && s2 < 0) || (s1 == 0 && s2 < 0)) continue;
    if (s1 * s2 < 0) {
      pt p;
      assert(intersect(pol[i], pol[nexti], a, b, p, true));
      ans.push_back(p);
      if (s2 > 0) ans.push_back(pol[nexti]);
      continue;
    }
    ans.push_back(pol[nexti]);
  }
  pol = ans;
}
int main() {
  cin >> n >> h >> f;
  focus = pt(0.0, f);
  mfocus = pt(0.0, -f);
  lftop = pt(-1e7, h);
  rgtop = pt(1e7, h);
  lfbot = pt(-1e7, -h);
  rgbot = pt(1e7, -h);
  for (int i = 0; i < int(n); i++) scanf("%d%d", &lf[i], &rg[i]);
  long double S = 0.0;
  for (int i = 0; i < int(n); i++) {
    vector<pt> pol;
    pt plf = pt(lf[i], h), prg = pt(rg[i], h);
    pt cur;
    assert(intersect(focus, plf, lftop, rgtop, cur, false));
    pol.push_back(cur);
    assert(intersect(focus, plf, lfbot, rgbot, cur, false));
    pol.push_back(cur);
    assert(intersect(focus, prg, lfbot, rgbot, cur, false));
    pol.push_back(cur);
    assert(intersect(focus, prg, lftop, rgtop, cur, false));
    pol.push_back(cur);
    long double spol = square(pol);
    S += 2.0 * spol;
    for (int j = 0; j < int(n); j++) {
      pt nplf = pt(lf[j], -h), nprg = pt(rg[j], -h);
      vector<pt> npol = pol;
      cut(npol, mfocus, nplf, nprg);
      cut(npol, mfocus, nprg, nplf);
      long double s = square(npol);
      if (s + EPS < spol) S -= s;
    }
  }
  cout << setprecision(10) << fixed;
  cout << S << endl;
  return 0;
}