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>
const long double eps = 1e-9;
const long double pi = acos(-1);
bool Equal(long double x, long double y) { return fabs(x - y) < eps; }
bool Greater(long double x, long double y) { return x - eps > y; }
bool Lesser(long double x, long double y) { return x + eps < y; }
struct point {
  long double x, y, ang;
};
using namespace std;
int main() {
  long long x1, y1, r1, x2, y2, r2;
  cin >> x1 >> y1 >> r1;
  cin >> x2 >> y2 >> r2;
  if (r1 < r2) {
    swap(r1, r2);
    swap(x1, x2);
    swap(y1, y2);
  }
  long long c1c2 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  cout << setprecision(10) << fixed;
  long double ans = 0.0, rr1, rr2;
  if (c1c2 >= (r1 + r2) * (r1 + r2)) {
    printf("0.000000000000");
    return 0;
  } else if (c1c2 <= (r1 - r2) * (r1 - r2)) {
    cout << pi * (long double)r2 * (long double)r2;
    return 0;
  }
  long double d = sqrt((long double)c1c2);
  rr1 = r1, rr2 = r2;
  long double th2 = acos((rr2 * rr2 + d * d - rr1 * rr1) / (2 * rr2 * d));
  long double th1 = acos((rr1 * rr1 + d * d - rr2 * rr2) / (2 * rr1 * d));
  long double second = th1 * rr1 * rr1;
  long double t = rr1 * rr1 * sin(th1) * cos(th1);
  ans += second - t;
  second = th2 * rr2 * rr2;
  t = rr2 * rr2 * sin(th2) * cos(th2);
  ans += second - t;
  cout << ans;
}