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 rep(i, n) for (int i = 0; i < (n); i++)
#define repr(i, n) for (int i = (n) - 1; i >= 0; i--)
#define range(a) a.begin(), a.end()

using point = complex<double>;

point gaisetu_tyusin(point a, point b, point c) {
  a -= c;
  b -= c;
  return a * b * (conj(a) - conj(b)) / (conj(a) * b - a * conj(b)) + c;
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  int N; cin >> N;
  vector<point> P(N);
  rep(i, N) {
    int x, y; cin >> x >> y;
    P[i] = point(x, y);
  }
  auto f = [&](point p) {
    double res = 0;
    rep(i, N) {
      res = max(res, abs(P[i] - p));
    }
    return res;
  };
  double ans = 1e100;
  rep(i, N) rep(j, i) {
    ans = min(ans, f((P[i] + P[j]) / 2.0));
    rep(k, j) {
      ans = min(ans, f(gaisetu_tyusin(P[i], P[j], P[k])));
    }
  }
  cout << ans << endl;
}