Problem: 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}.

Examples

Input

2
0 0
1 0


Output

0.500000000000000000


Input

3
0 0
0 1
1 0


Output

0.707106781186497524


Input

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9


Output

6.726812023536805158

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
int main()
{
        ios::sync_with_stdio(0);
        cin.tie(0);
        int n{0};
        double X{0},Y{0};
        cin>>n;
        vector<double> x(n),y(n);
        for(int i =0;i<n;i++)
        {
                cin>>x[i]>>y[i];
                X += x[i];
                Y += y[i];
        }
        X = X/n;
        Y /= n;
        double p = 0.1;
        double d{0};
        for(int i =0;i<30000;i++)
        {
                int f{0};
                d =(X - x[0])*(X - x[0]) + (Y - y[0])*(Y-y[0]); 
                for(int j = 1;j<n;j++)
                {
                        double e = (X - x[j])*(X - x[j]) + (Y - y[j])*(Y-y[j]);
                        if( e > d)
                        {
                                d=e;
                                f = j;
                        }
                }
                X += (x[f] - X)*p;
                Y += (y[f] - Y)*p;
                p *= .999;
        }
        cout<<fixed<<setprecision(20)<<sqrt(d);



        return 0;
}