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>

#define _GLIBCXX_DEBUG
#define all(v) (v).begin(),(v).end()

using namespace std;

using ll=long long;
using pii=pair<int, int>;
using vi=vector<int>;

const ll INF=1LL<<60;
const ll MOD=1e9+7;

int main(){
    int N; cin >> N;
    vector<double> x(N), y(N);
    for(int i=0; i<N; i++){
        cin >> x[i] >> y[i];
    }
    double res=1e10;
    if(N == 2){
        res=sqrt(pow(x[0]-x[1], 2)+pow(y[0]-y[1], 2))/2;
    }
    for(int i=0; i<N-2; i++){
        for(int j=i+1; j<N-1; j++){
            for(int k=j+1; k<N; k++){
                double R;
                double a, b, c;
                a=pow(x[i]-x[j], 2)+pow(y[i]-y[j], 2);
                b=pow(x[j]-x[k], 2)+pow(y[j]-y[k], 2);
                c=pow(x[k]-x[i], 2)+pow(y[k]-y[i], 2);
                double val=a*(b+c-a)+b*(c+a-b)+c*(a+b-c);
                double ux, uy;
                if(val == 0){
                    R=sqrt(max(a, max(b, c)))/2;
                    ux=(min(x[i], min(x[j], x[k]))+max(x[i], max(x[j], x[k])))/2;
                    uy=(min(y[i], min(y[j], y[k]))+max(y[i], max(y[j], y[k])))/2;
                }
                else{
                    ux=(a*(b+c-a)*x[k]+b*(c+a-b)*x[i]+c*(a+b-c)*x[j])/val;
                    uy=(a*(b+c-a)*y[k]+b*(c+a-b)*y[i]+c*(a+b-c)*y[j])/val;
                    a=sqrt(a), b=sqrt(b), c=sqrt(c);
                    R=a*b*c/sqrt((a+b+c)*(-a+b+c)*(a-b+c)*(a+b-c));
                }
                bool ok=true;
                for(int l=0; l<N; l++){
                    if(l == i || l == j || l == k) continue;
                    double dist=pow(x[l]-ux, 2)+pow(y[l]-uy, 2);
                    if(dist > R*R) ok=false;
                }
                if(ok) res=min(res, R);
            }
        }
    }
    printf("%.6f\n",res);
    return 0;
}