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;
vector<pair<pair<int, int>, char> > vpp;
vector<pair<int, int> > vp;
const int INF = 1e9;
long double caldis(long double x1, long double y1, long double x2,
                   long double y2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
long double solve_cos(long double a, long double b, long double c) {
  return acos((a * a + b * b - c * c) / (2 * a * b));
}
long double intersect(long double ang, long double r) {
  long double s1, s2;
  s1 = ang * r * r / 2;
  s2 = sin(ang) * r * r / 2;
  return s1 - s2;
}
int main() {
  long double x1, x2, r1, r2, y1, y2;
  cin >> x1 >> y1 >> r1 >> x2 >> y2 >> r2;
  if (r1 < r2) {
    swap(x1, x2);
    swap(y1, y2);
    swap(r1, r2);
  }
  long double dis = caldis(x1, y1, x2, y2);
  if (dis + r2 <= r1 + 1e-16) {
    cout << setprecision(15);
    cout << (r2 * r2) * acos(-1.0) << endl;
  } else if (dis >= r1 + r2 - 1e-16) {
    cout << 0 << endl;
  } else {
    long double ang1 = solve_cos(dis, r1, r2);
    long double ang2 = solve_cos(dis, r2, r1);
    long double part1 = intersect(ang1 * 2.0, r1);
    part1 += (intersect(ang2 * 2.0, r2));
    cout << setprecision(15);
    cout << part1 << endl;
  }
  return 0;
}