Problem: You are given two circles. Find the area of their intersection.

Input

The first line contains three integers x1, y1, r1 ( - 109 ≤ x1, y1 ≤ 109, 1 ≤ r1 ≤ 109) — the position of the center and the radius of the first circle.

The second line contains three integers x2, y2, r2 ( - 109 ≤ x2, y2 ≤ 109, 1 ≤ r2 ≤ 109) — the position of the center and the radius of the second circle.

Output

Print the area of the intersection of the circles. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Examples

Input

0 0 4
6 0 4


Output

7.25298806364175601379


Input

0 0 5
11 0 5


Output

0.00000000000000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const auto start_time = std::chrono::high_resolution_clock::now();
void timecalculater() {}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
void __print(int x) { cout << x; }
void __print(long x) { cout << x; }
void __print(long long x) { cout << x; }
void __print(unsigned x) { cout << x; }
void __print(unsigned long x) { cout << x; }
void __print(unsigned long long x) { cout << x; }
void __print(float x) { cout << x; }
void __print(double x) { cout << x; }
void __print(long double x) { cout << x; }
void __print(char x) { cout << '\'' << x << '\''; }
void __print(const char *x) { cout << '\"' << x << '\"'; }
void __print(const string &x) { cout << '\"' << x << '\"'; }
void __print(bool x) { cout << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cout << '{';
  __print(x.first);
  cout << ',';
  __print(x.second);
  cout << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cout << '{';
  for (auto &i : x) cout << (f++ ? "," : ""), __print(i);
  cout << "}";
}
void _print() { cout << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cout << ", ";
  _print(v...);
}
long long p = 1e9 + 7;
const int N = 2e5 + 5;
long double dis(long double x1, long double y1, long double x2,
                long double y2) {
  long double x = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
  return sqrt(x);
}
int main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cin.exceptions(cin.failbit);
  ;
  int T = 1;
  while (T--) {
    long double x1, y1, r1;
    cin >> x1 >> y1 >> r1;
    long double x2, y2, r2;
    cin >> x2 >> y2 >> r2;
    long double ans = 0;
    long double d = dis(x1, y1, x2, y2);
    long double d1 = (r1 * r1 - r2 * r2) / (2 * d) + d / 2;
    long double d2 = (r2 * r2 - r1 * r1) / (2 * d) + d / 2;
    long double pi = acos(-1);
    if (d <= (r1 - r2)) {
      ans = pi * r2 * r2;
    } else if (d <= (r2 - r1)) {
      ans = pi * r1 * r1;
    } else if (d < (r1 + r2)) {
      long double alpha = acos((r2 * r2 + d * d - r1 * r1) / (2 * r2 * d));
      long double s = alpha * r2 * r2;
      long double t = r2 * r2 * sin(alpha) * cos(alpha);
      long double ans1, ans2;
      ans1 = s - t;
      alpha = acos((r1 * r1 + d * d - r2 * r2) / (2 * r1 * d));
      s = alpha * r1 * r1;
      t = r1 * r1 * sin(alpha) * cos(alpha);
      ans2 = s - t;
      ans = ans1 + ans2;
    }
    cout << fixed << setprecision(9);
    cout << ans;
  }
  timecalculater();
  return 0;
}