Problem: Given are N points (x_i, y_i) in a two-dimensional plane.

Find the minimum radius of a circle such that all the points are inside or on it.

Constraints

* 2 \leq N \leq 50
* 0 \leq x_i \leq 1000
* 0 \leq y_i \leq 1000
* The given N points are all different.
* The values in input are all integers.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
:
x_N y_N


Output

Print the minimum radius of a circle such that all the N points are inside or on it.

Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.

Examples

Input

2
0 0
1 0


Output

0.500000000000000000


Input

3
0 0
0 1
1 0


Output

0.707106781186497524


Input

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9


Output

6.726812023536805158

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define fcout cout << fixed << setprecision(18)

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  double N; cin >> N;
  double ax = 0.0, ay = 0.0;
  vector<double> x(N), y(N);
  for (int i = 0; i < N; i++) {
    cin >> x[i] >> y[i];
    ax += x[i];
    ay += y[i];
  }

  ax /= N;
  ay /= N;

  double max;
  double m = 1.0;
  while (m > 1e-8) {
    int k;
    for (int t = 0; t < 100; t++) {
      max = 0.0;
      for (int i = 0; i < N; i++) {
        double temp = (ax - x[i]) * (ax - x[i]) + (ay - y[i]) * (ay - y[i]);
        if (max < temp) {
          k = i;
          max = temp;
        }
      }
      ax += (x[k] - ax) * m;
      ay += (y[k] - ay) * m;
    }
    m /= 1.5;
  }

  double ans = sqrt(max);
  fcout << ans << '\n';
  return 0;
}