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;
using ull = unsigned long long;
using P = pair<int,int>;
#define rep(i,n) for(ll i = 0;i < (ll)n;i++)
#define ALL(x) (x).begin(),(x).end()
#define MOD 1000000007

int x[55],y[55];
int n;

double sq(double d){return d*d;}

double d(double X,double Y){
  double res = 0;
  rep(i,n){
    res = max(res,sqrt(sq(X-x[i])+sq(Y-y[i])));
  }
  return res;
}

double cal(double X){
  double l = 0,r = 1000;
  rep(i,100){
    double ml = (l*2+r)/3,mr = (l+r*2)/3;
    if(d(X,ml) >= d(X,mr))l = ml;
    else r = mr;
  }
  return d(X,l);
}

int main(){
  
  cout << fixed << setprecision(20);
  cin >> n;
  rep(i,n)cin >> x[i] >> y[i];
  double l = 0,r = 1000;
  rep(i,100){
    double ml = (l*2+r)/3,mr = (l+r*2)/3;
    if(cal(ml) >= cal(mr))l = ml;
    else r = mr;
  }
  cout << cal(l) << endl;
  

  return 0;
}