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 ll long long
#define dl double
using namespace std;

//***********************************************************************
int MAXNUM = 5e3+5;
vector <int>vis(MAXNUM);
vector<int> pr;
void sieve() {
	pr.push_back(2);
	for(ll i=3;i<MAXNUM;i+=2) if(!vis[i]) {
		pr.push_back(i);
		for(ll j=i*i;j<MAXNUM;j+=2*i) vis[j]=true;
	}
}
//************************************************************************

void solve()
{
    int n;
    cin >> n;
    vector<dl> a(n);
    vector<dl> b(n);
    for(int i=0;i<n;i++)
    {
        cin >> a[i] >> b[i];

    }
    dl ans=0;
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<n;j++)
        {
            if(ans*ans<((a[i]-a[j])*(a[i]-a[j])+(b[i]-b[j])*(b[i]-b[j])))
            {
                ans=sqrt((a[i]-a[j])*(a[i]-a[j])+(b[i]-b[j])*(b[i]-b[j]));
            }
        }
    }
    cout << setprecision(25) << fixed << ans/2.0 << endl;
	
}


int main()
{ 
	ios_base::sync_with_stdio(false); 
    cin.tie(NULL);
	ll t;
	//cin >> t;
	t=1;
	while(t--)
	{
		solve();
	}

	return 0;
}