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;

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

  int N; cin>>N;
  vector<pair<double, double>> dot(N);
  for (auto& p : dot) {
    cin>>p.first>>p.second;
  }

  auto min_range = [&](double x, double y) {
    double r = 0;
    for (auto d : dot) {
      auto cr = sqrt(pow(d.first-x, 2) + pow(d.second-y, 2));
      r = max(cr, r);
    }
    return r;
  };

  const double phi = (sqrt(5)+1)/2;
  auto min_range_x = [&](double x) {
    double l = 0, h = 1000;
    for (int i = 0; i < 80; i++) {
      auto cl = (l*phi+h)/(phi+1);
      auto ch = (l+h*phi)/(phi+1);
      auto rl = min_range(x, cl);
      auto rh = min_range(x, ch);
      if (rl > rh) {
        l = cl;
      } else {
        h = ch;
      }
    }
    return min_range(x, (l+h)/2);
  };
  double l = 0, r = 1000;
  double ans;
  for (int i = 0; i < 80; i++) {
    auto cl = (l*phi+r)/(phi+1);
    auto cr = (l+r*phi)/(phi+1);
    auto rl = min_range_x(cl);
    auto rh = min_range_x(cr);
    if (rl > rh) {
      l = cl;
      ans = rh;
    } else {
      r = cr;
      ans = rl;
    }
  }
  cout << fixed << ans << endl;

  return 0;
}