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 rep(i,n) for (int i=0;i<(n);++i)
using namespace std;
 
double distance(double x1, double y1, double x2, double y2){
  return sqrt(pow(x1-x2,2) + pow(y1-y2,2));
    
}
 
int main(){
  int n;
  cin >> n;
  double max_val = 0;
  vector<double> x(n);
  vector<double> y(n);
    
  rep(i,n) cin >> x.at(i) >> y.at(i);
  
  rep(i,n-1){
    for(int j=i+1;j<n;j++){
      double tmp;
      tmp = distance(x.at(i), y.at(i), x.at(j), y.at(j));
      max_val = max(tmp, max_val);
    }
  }
  printf("%.18f", max_val/2);
}