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;

double x[12345], y[12345];
double dis[12345];
double minRadius(int k, int n)
{
   double ans = 0.000000000;
   for(int i = 0; i < n; i++)
   {
       for(int j = 0; j < n; j++)
       {
           double X  = (x[i] - x[j]) * (x[i] - x[j]) + (y[i] - y[j]) * (y[i] - y[j]);
           //X = sqrt( X );
           double tmp = 0.000000000000;
            ans = max(X, ans);
       }
   }
    sort(dis, dis + n);

    cout<<setprecision(18)<<fixed<<sqrt(ans)/2.0;
}

int main()
{
  int n;
  cin>>n;
  for(int i = 0; i < n; i++) cin>>x[i]>>y[i];
  minRadius(n, n);
  return 0;
}