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 int inf=1e9+7;
const ll INF=1LL<<61;
const ll mod=1e9+7;

int n;
double x[1010],y[1010];

double ly,ry;

double solve(double px){
  ly=-1000.0;
  ry=2000.0;
  while(1){
    double sy=(2*ly+ry)/3.0;
    double ty=(ly+2*ry)/3.0;
    double ss,tt;
    ss=0.0,tt=0.0;
    for(int i=0;i<n;i++){
      ss=max(ss,sqrt((px-x[i])*(px-x[i])+(sy-y[i])*(sy-y[i])));
      tt=max(tt,sqrt((px-x[i])*(px-x[i])+(ty-y[i])*(ty-y[i])));
    }
    //cout<<ss<<endl;
    if(ry-ly<=1e-10) {
      //cout<<ss<<endl;
      return ss;
    }
    if(ss<=tt) ry=ty;
    else ly=sy;
  }
}

int main(){
  int i,j;
  cin>>n;
  for(i=0;i<n;i++) cin>>x[i]>>y[i];
  double lx=-1000.0,rx=2000.0;
  while(1){
    double sx=(2*lx+rx)/3.0;
    double tx=(lx+2*rx)/3.0;
    if(rx-lx<=1e-10) {
      cout<<fixed<<setprecision(15)<<solve(sx)<<endl;
      return 0;
    }
    if(solve(sx)<=solve(tx)) rx=tx;
    else lx=sx;
  }

  return 0;
}