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:268435456")
using namespace std;
template <typename T>
T sqr(const T& x) {
  return x * x;
}
template <typename T>
T my_abs(const T& x) {
  return x < 0 ? -x : x;
}
const int INF = (int)1e9;
const long long LINF = (long long)6e18;
const long long INF64 = LINF;
const long long INFLL = LINF;
const long double EPS = 1e-7;
const long double PI = 3.1415926535897932384626433832795;
const long double ME = 1e-5;
const long long MOD = (int)1e9 + 7;
const long long MOD2 = (int)1e9 + 21;
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
const int SQN = 500;
const int LOGN = 17;
const int N = (int)1e3 + 10;
struct line {
  long double A, B, C;
};
inline line get_line(const pair<long double, long double>& a,
                     const pair<long double, long double>& b) {
  line result;
  result.A = b.second - a.second;
  result.B = a.first - b.first;
  result.C = -result.A * a.first - result.B * a.second;
  return result;
}
inline pair<long double, long double> operator+(
    const pair<long double, long double>& a,
    const pair<long double, long double>& b) {
  return pair<long double, long double>(a.first + b.first, a.second + b.second);
}
inline pair<long double, long double> operator-(
    const pair<long double, long double>& a,
    const pair<long double, long double>& b) {
  return pair<long double, long double>(a.first - b.first, a.second - b.second);
}
inline pair<long double, long double> operator*(
    const pair<long double, long double>& a, long double k) {
  return pair<long double, long double>(a.first * k, a.second * k);
}
inline long double cp(const pair<long double, long double>& a,
                      const pair<long double, long double>& b) {
  return a.first * b.second - a.second * b.first;
}
inline bool intersect(const line& a, const line& b,
                      pair<long double, long double>& res) {
  long double d = cp(pair<long double, long double>(a.A, a.B),
                     pair<long double, long double>(b.A, b.B));
  if (abs(d) < EPS) {
    return false;
  }
  res.first = -cp(pair<long double, long double>(a.C, a.B),
                  pair<long double, long double>(b.C, b.B)) /
              d;
  res.second = -cp(pair<long double, long double>(a.A, a.C),
                   pair<long double, long double>(b.A, b.C)) /
               d;
  return true;
}
inline long double dist(const pair<long double, long double>& a,
                        const pair<long double, long double>& b) {
  return sqrt(sqr(a.first - b.first) + sqr(a.second - b.second));
}
inline bool equals(const pair<long double, long double>& a,
                   const pair<long double, long double>& b) {
  return dist(a, b) < EPS;
}
inline long double get_area(vector<pair<long double, long double> >& p) {
  if (int(p.size()) < 3) {
    return 0;
  }
  pair<long double, long double> c(0, 0);
  for (int i = 0; i < int(int(p.size())); ++i) {
    c = c + (p[i] * (1.0 / (long double)int(p.size())));
  }
  for (int i = 0; i < int(int(p.size())); ++i) {
    p[i] = p[i] - c;
  }
  vector<pair<long double, pair<long double, long double> > > pp;
  for (int i = 0; i < int(int(p.size())); ++i) {
    pp.push_back(make_pair((long double)atan2(p[i].second, p[i].first), p[i]));
  }
  sort(pp.begin(), pp.end());
  for (int i = 0; i < int(int(p.size())); ++i) {
    p[i] = pp[i].second;
  }
  p.erase(unique(p.begin(), p.end(), equals), p.end());
  long double res = 0;
  for (int i = 0; i < int(int(p.size())); ++i) {
    int j = (i + 1) % int(p.size());
    res += cp(p[i] - c, p[j] - c);
  }
  return abs(res) / 2.0;
}
vector<pair<long double, long double> > s;
long double ans = 0;
inline void solve() {
  int n;
  long double h, f;
  cin >> n >> h >> f;
  for (int i = 0; i < int(n); ++i) {
    int l, r;
    cin >> l >> r;
    if (l < 0 && r > 0) {
      s.push_back(pair<long double, long double>(l, 0));
      s.push_back(pair<long double, long double>(0, r));
    } else {
      s.push_back(pair<long double, long double>(l, r));
    }
  }
  pair<long double, long double> cu = pair<long double, long double>(0, f);
  pair<long double, long double> cd = pair<long double, long double>(0, -f);
  line ul = get_line(pair<long double, long double>(0, h),
                     pair<long double, long double>(1, h));
  line dl = get_line(pair<long double, long double>(0, -h),
                     pair<long double, long double>(1, -h));
  for (int i = 0; i < int(int(s.size())); ++i) {
    pair<long double, long double> lp =
        pair<long double, long double>(s[i].first, -h);
    pair<long double, long double> rp =
        pair<long double, long double>(s[i].second, -h);
    line l = get_line(cd, lp);
    line r = get_line(cd, rp);
    pair<long double, long double> ulp;
    intersect(l, ul, ulp);
    pair<long double, long double> urp;
    intersect(r, ul, urp);
    ans += h * (s[i].second - s[i].first + urp.first - ulp.first);
  }
  ans *= 2.0;
  for (int i = 0; i < int(int(s.size())); ++i) {
    for (int j = 0; j < int(i + 1); ++j) {
      vector<pair<long double, long double> > pts;
      pair<long double, long double> lp1 =
          pair<long double, long double>(s[i].first, -h);
      pair<long double, long double> rp1 =
          pair<long double, long double>(s[i].second, -h);
      line l1 = get_line(cd, lp1);
      line r1 = get_line(cd, rp1);
      pair<long double, long double> ulp1;
      intersect(l1, ul, ulp1);
      pair<long double, long double> urp1;
      intersect(r1, ul, urp1);
      pair<long double, long double> lp2 =
          pair<long double, long double>(s[j].first, h);
      pair<long double, long double> rp2 =
          pair<long double, long double>(s[j].second, h);
      line l2 = get_line(cu, lp2);
      line r2 = get_line(cu, rp2);
      pair<long double, long double> dlp2;
      intersect(l2, dl, dlp2);
      pair<long double, long double> drp2;
      intersect(r2, dl, drp2);
      if (ulp1.first >= lp2.first && ulp1.first <= rp2.first) {
        pts.push_back(ulp1);
      }
      if (urp1.first >= lp2.first && urp1.first <= rp2.first) {
        pts.push_back(urp1);
      }
      if (dlp2.first >= lp1.first && dlp2.first <= rp1.first) {
        pts.push_back(dlp2);
      }
      if (drp2.first >= lp1.first && drp2.first <= rp1.first) {
        pts.push_back(drp2);
      }
      if (lp2.first >= ulp1.first && lp2.first <= urp1.first) {
        pts.push_back(lp2);
      }
      if (rp2.first >= ulp1.first && rp2.first <= urp1.first) {
        pts.push_back(rp2);
      }
      if (lp1.first >= dlp2.first && lp1.first <= drp2.first) {
        pts.push_back(lp1);
      }
      if (rp1.first >= dlp2.first && rp1.first <= drp2.first) {
        pts.push_back(rp1);
      }
      pair<long double, long double> cll;
      if (intersect(l1, l2, cll) && cll.second >= -h && cll.second <= h) {
        pts.push_back(cll);
      }
      pair<long double, long double> clr;
      if (intersect(l1, r2, clr) && clr.second >= -h && clr.second <= h) {
        pts.push_back(clr);
      }
      pair<long double, long double> crl;
      if (intersect(r1, l2, crl) && crl.second >= -h && crl.second <= h) {
        pts.push_back(crl);
      }
      pair<long double, long double> crr;
      if (intersect(r1, r2, crr) && crr.second >= -h && crr.second <= h) {
        pts.push_back(crr);
      }
      if (i == j) {
        ans -= get_area(pts);
      } else {
        ans -= 2.0 * get_area(pts);
      }
    }
  }
  cout << ans << endl;
}
int main() {
  srand((unsigned int)time(NULL));
  cout << setprecision(15) << fixed;
  solve();
  cerr << "time: " << clock() << " ms" << endl;
  return 0;
}