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;
struct point {
  long double x, y;
  point(long double xx, long double yy) {
    x = xx;
    y = yy;
  }
};
const long double pi = acos(-1);
long double dist(point p1, point p2) { return hypot(p1.x - p2.x, p1.y - p2.y); }
int main() {
  cout << fixed << setprecision(12);
  long double x1, y1, r1;
  long double x2, y2, r2;
  cin >> x1 >> y1 >> r1;
  cin >> x2 >> y2 >> r2;
  point center1(x1, y1);
  point center2(x2, y2);
  if (r1 > r2) {
    swap(r1, r2);
    swap(center1, center2);
  }
  long double d = dist(center1, center2);
  if (d + r1 <= r2 + 1e-16) {
    long double ans = pi * r1 * r1;
    cout << ans << endl;
  } else {
    if (d + 1e-16 >= r1 + r2) {
      cout << 0.0 << endl;
    } else {
      long double ang1 = acos((d * d + r1 * r1 - r2 * r2) / (2.0 * d * r1));
      long double sect1 = ang1 * r1 * r1;
      long double tri1 = r1 * r1 * cos(ang1) * sin(ang1);
      long double ans1 = sect1 - tri1;
      long double ang2 = acos((d * d + r2 * r2 - r1 * r1) / (2.0 * d * r2));
      long double sect2 = ang2 * r2 * r2;
      long double tri2 = r2 * r2 * cos(ang2) * sin(ang2);
      long double ans2 = sect2 - tri2;
      cout << ans1 + ans2 << endl;
    }
  }
  return 0;
}