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-9;
long long xc1, yc1, xc2, yc2, r1, r2;
long double yt1, xt1, yt2, xt2, area = 0;
long double dist(long long x1, long long y1, long long x2, long long y2) {
  long double d = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  return d;
}
bool check(long long x1, long long y1, long long r1, long long x2, long long y2,
           long long r2) {
  long double d = dist(x1, y1, x2, y2);
  d = sqrt(d);
  if (d + r1 - r2 <= eps)
    return true;
  else if (d + r2 - r1 <= eps)
    return true;
  return false;
}
long double calcArea(long long xc1, long long yc1, long long xc2, long long yc2,
                     long long r1, long long r2) {
  long double c = sqrt(dist(xc1, yc1, xc2, yc2));
  long double d = (r1 * r1 - r2 * r2) / (2 * c) + c / 2;
  long double co1 = d / r1;
  long double co2 = (c - d) / r2;
  long double ang1 = 2 * acos(co1);
  long double ang2 = 2 * acos(co2);
  long double a1 = ang1 * r1 * r1 / 2 - sin(ang1) * r1 * r1 / 2;
  long double a2 = ang2 * r2 * r2 / 2 - sin(ang2) * r2 * r2 / 2;
  long double A = a1 + a2;
  return A;
}
int32_t main() {
  cout << setprecision(12) << fixed;
  cin >> xc1 >> yc1 >> r1 >> xc2 >> yc2 >> r2;
  if (check(xc1, yc1, r1, xc2, yc2, r2)) {
    if (r1 < r2) {
      area = acos(-1) * r1 * r1;
      cout << area << '\n';
    } else {
      area = acos(-1) * r2 * r2;
      cout << area << '\n';
    }
  } else {
    if (sqrt(dist(xc1, yc1, xc2, yc2)) - (r1 + r2) >= eps)
      cout << .0 << '\n';
    else {
      area = calcArea(xc1, yc1, xc2, yc2, r1, r2);
      cout << area << '\n';
    }
  }
}