Problem:
Score : 600 points

Problem Statement

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}.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
using datas=pair<ll,ll>;
using ddatas=pair<double,double>;
using tdata=pair<ll,datas>;
using vec=vector<ll>;
using mat=vector<vec>;
using pvec=vector<datas>;
using pmat=vector<pvec>;
#define For(i,a,b) for(i=a;i<(ll)b;i++)
#define bFor(i,a,b) for(i=a;i>=(ll)b;i--)
#define rep(i,N) For(i,0,N)
#define rep1(i,N) For(i,1,N)
#define brep(i,N) bFor(i,N-1,0)
#define all(v) (v).begin(),(v).end()
#define allr(v) (v).rbegin(),(v).rend()
#define vsort(v) sort(all(v))
#define vrsort(v) sort(allr(v))
#define endl "\n"
#define pb push_back
#define print(v) cout<<v<<endl
#define printyes cout<<"Yes"<<endl
#define printno cout<<"No"<<endl
#define printYES cout<<"YES"<<endl
#define printNO cout<<"NO"<<endl
#define output(v) do{bool f=0;for(auto outi:v){cout<<(f?" ":"")<<outi;f=1;}cout<<endl;}while(0)
const ll mod=1000000007;
const ll inf=1LL<<60;
const double PI = acos(-1);
const double eps = 1e-15;
template<class T> inline bool chmax(T& a,T b){bool x=a<b;if(x)a=b;return x;} 
template<class T> inline bool chmin(T& a,T b){bool x=a>b;if(x)a=b;return x;} 

void startupcpp(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout<<fixed<<setprecision(15);
}
struct Point{double x,y;};
double dis(Point a,Point b){
  return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
Point tri(Point a, Point b, Point c){
  double a1,a2,b1,b2,c1,c2;
  a1=2*(b.x-a.x);
  b1=2*(b.y-a.y);
  c1=a.x*a.x-b.x*b.x+a.y*a.y-b.y*b.y;
  a2=2*(c.x-a.x);
  b2=2*(c.y-a.y);
  c2=a.x*a.x-c.x*c.x+a.y*a.y-c.y*c.y;
  Point p;
  p.x=(b1*c2-b2*c1)/(a1*b2-a2*b1);
  p.y=(c1*a2-c2*a1)/(a1*b2-a2*b1);
  return p;
}
int main(){
  startupcpp();
  // ll test;cin>>test;while(test--){
  ll i,j,k,l,N;
  cin>>N;
  double ans=inf,fir;
  vector<Point> v(N);
  Point x;
  rep(i,N)cin>>v[i].x>>v[i].y;
  sort(all(v),[](auto const& a,auto const& b){if(a.x!=b.x){return a.x>b.x;}else if(a.y!=b.y){return a.y<b.y;}else{return true;}});
  rep(i,N)For(j,i+1,N){
    double res=dis(v[i],v[j])*0.5;
    fir=res;
    x.x=(v[i].x+v[j].x)/2;
    x.y=(v[i].y+v[j].y)/2;
    rep(k,N){
      if(i==k||j==k)continue;
      if(dis(x,v[k])>fir+eps){
        res=inf;
        break;
      }
    }
    chmin(ans,res);
  }
  rep(i,N)For(j,i+1,N)For(k,j+1,N){
    if((v[i].x-v[k].x)*(v[j].y-v[k].y)!=(v[i].y-v[k].y)*(v[j].x-v[k].x)){
      x=tri(v[i],v[j],v[k]);
      fir=dis(x,v[i]);
      rep(l,N){
        if(dis(x,v[l])>fir+eps){
        fir=inf;
        break;
        }
      }
      chmin(ans,fir);
    }
  }
  print(ans);
  return 0;
}