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 long double eps = 1e-12;
const long double PI = 2 * acos(0);
long double solve(long double r1, long double r2, long double d) {
  long double lo = 0;
  long double hi = PI;
  for (int it = 0; it < 1000; it++) {
    long double mid = (lo + hi) / 2.0;
    long double x = r1 * cos(mid) - d;
    long double y = r1 * sin(mid);
    if (x * x + y * y <= r2 * r2 + eps)
      lo = mid;
    else
      hi = mid;
  }
  return (lo + hi) / 2.0;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.precision(12);
  long double x1, x2, y1, y2, r1, r2;
  cin >> x1 >> y1 >> r1 >> x2 >> y2 >> r2;
  if (r1 > r2) {
    swap(x1, x2);
    swap(y1, y2);
    swap(r1, r2);
  }
  long double dx = x1 - x2;
  long double dy = y1 - y2;
  long double d = sqrt(dx * dx + dy * dy);
  if (d - eps >= r1 + r2) {
    cout << fixed << 0.0 << '\n';
    return 0;
  }
  if (d + r1 <= r2 + eps) {
    cout << fixed << PI * r1 * r1 << '\n';
    return 0;
  }
  long double angle = solve(r1, r2, d);
  long double ans = r1 * r1 * angle;
  if (angle <= PI / 2.0)
    ans -= r1 * r1 * sin(2.0 * angle) / 2.0;
  else
    ans += r1 * r1 * sin(2.0 * PI - 2.0 * angle) / 2.0;
  angle = solve(r2, r1, d);
  ans += r2 * r2 * angle;
  if (angle <= PI / 2.0)
    ans -= r2 * r2 * sin(2.0 * angle) / 2.0;
  else
    ans += r2 * r2 * sin(2.0 * PI - 2.0 * angle) / 2.0;
  cout << fixed << ans << '\n';
}