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;
const int nmax=52;
double x[nmax],y[nmax];
double d(int a,int b){
  return sqrt((x[a]-x[b])*(x[a]-x[b])+(y[a]-y[b])*(y[a]-y[b]));
}
double f(int a,int b,int c){
  vector<double> p(3);
  p[0]=d(a,b),p[1]=d(b,c),p[2]=d(c,a);
  sort(p.begin(),p.end());
  double co=(p[0]*p[0]+p[1]*p[1]-p[2]*p[2])/(2*p[0]*p[1]);
  if(co<=0){
    return p[2]/2;
  }
  double si=sqrt(1-co*co);
  return p[2]/2/si;
}
int main(){
  int n;cin >> n;
  double ans=0;
  for(int i=0;i<n;i++){
    cin >> x[i] >> y[i];
  }
  if(n==2){
    ans=d(0,1)/2;
  }
  else{
  for(int i=0;i<n;i++){
    for(int j=i+1;j<n;j++){
      for(int k=j+1;k<n;k++){
        if(i!=j&&i!=k&&j!=k){
        ans=max(ans,f(i,j,k));
        }
      }
    }
  }
  }
  cout << fixed << setprecision(15) << ans << endl;
}