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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define f(i,x,n) for(int i=x;i<(int)(n);++i)
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=100005,INF=1<<29;

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int N;cin>>N;
    vector<long double> X(N),Y(N);
    long double ans=INF;
    
    for(int i=0;i<N;i++){
        cin>>X[i]>>Y[i];
    }
    
    if(N==2){
        cout<<setprecision(25)<<hypot(X[0]-X[1],Y[0]-Y[1])/2.0<<endl;
    }else{
        for(int i=0;i<N;i++){
            for(int j=i+1;j<N;j++){
                for(int k=j+1;k<N;k++){
                    long double a=X[i],b=Y[i],c=X[j],d=Y[j],e=X[k],f=Y[k];
                    long double x,y;
                    
                    x=0.5*((a*a+b*b)*(d-f)+(c*c+d*d)*(f-b)+(e*e+f*f)*(b-d))/((a*(d-f)+c*(f-b)+e*(b-d)));
                    y=0.5*((a*a+b*b)*(e-c)+(c*c+d*d)*(a-e)+(e*e+f*f)*(c-a))/((a*(d-f)+c*(f-b)+e*(b-d)));
                    
                    long double maxi=0.0;
                    
                    for(int l=0;l<N;l++){
                        maxi=max(maxi,hypot(X[l]-x,Y[l]-y));
                    }
                    
                    ans=min(ans,maxi);
                    
                    //cout<<maxi<<endl;
                }
            }
        }
        
        cout<<setprecision(25)<<ans<<endl;
    }
}