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<cmath>
#include<cstdio>
#include<algorithm>

#define N 51

using namespace std;

#define eps 1e-18
#define delta 0.98
#define T 100

int n;
struct Point
{
    double x,y,z;
};
Point P[N];
double ans;

double dist(Point A,Point B)
{
    return sqrt((A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y));
}

double solve()
{
    double t;
    Point s=P[0];
    int k; double mx,res;
    int u=10;
    ans=1e20;
    while(u--)
    { 
	    t=T;
		while(t>eps)
	    {
	        mx=0;
	        for(int i=1;i<=n;i++)
	        {
	            res=dist(s,P[i]);
	            if(res>mx) mx=res,k=i;
	        }
	        ans=min(ans,mx);
	        s.x+=(P[k].x-s.x)/mx*t;
	        s.y+=(P[k].y-s.y)/mx*t;
	        t*=delta;
	    }
	} 
    return ans;
}

int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++) 
	{
		scanf("%lf%lf",&P[i].x,&P[i].y);
		P[0].x+=P[i].x;
		P[0].y+=P[i].y;
	}
	P[0].x/=n;
	P[0].y/=n;
    printf("%.10lf\n",solve());
}