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;
typedef long long ll;
#define pb push_back
#define fi first
#define se second

typedef pair<ll,ll> P;
using VP = vector<P>; using VVP = vector<VP>;
using VI = vector<int>; using VVI = vector<VI>; using VVVI = vector<VVI>;
const long double inf=1e9+7;
const ll INF=1LL<<61;
const ll mod=1e9+7;

double x[55],y[55];
double dif(int i,int j){
  return sqrt((x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]));
}


int main(){
  int i,j,k;
  int n;
  cin>>n;
  for(i=0;i<n;i++){
    cin>>x[i]>>y[i];
  }
  x[n]=0,y[n]=0;
  double l=500;
  while(l>1e-68){
    double md=-1;
    int ind;
    for(i=0;i<n;i++){
      if(md<dif(i,n)){
        md=dif(i,n);
        ind=i;
      }
    }
    x[n]=x[n]+l*(x[ind]-x[n])/md;
    y[n]=y[n]+l*(y[ind]-y[n])/md;
    l*=0.995;
  }
  double md=-1;
  int ind;
  for(i=0;i<n;i++){
    if(md<dif(i,n)){
        md=dif(i,n);
        ind=i;
    }
  }

  cout<<fixed<<setprecision(15)<<md<<endl;
  
  return 0;
}