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 int64 = long long;

constexpr int DEBUG = 0;

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

  cout << fixed << setprecision(10);

  int n;
  cin >> n;
  vector<double> xs(n), ys(n);
  for (int i = 0; i < n; i++) {
    cin >> xs[i] >> ys[i];
  }
  double x = 0, y = 0;
  double alpha = 1E6;
  while (true) {
    double max_d = 0;
    int max_arg = -1;
    for (int i = 0; i < n; i++) {
      double dx = xs[i] - x;
      double dy = ys[i] - y;
      double d = sqrt(dx * dx + dy * dy);
      if (d > max_d) {
        max_d = d;
        max_arg = i;
      }
    }

    if (alpha < 1E-12) {
      cout << max_d << endl;
      return 0;
    }

    x += (xs[max_arg] - x) / max_d * alpha;
    y += (ys[max_arg] - y) / max_d * alpha;
    alpha *= 0.99;
  }
}