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;
typedef long long lt;
typedef double dd;
#define eps 1e-6
#define sqr(x) ((x)*(x))


const int maxn=10010;
int n;
struct point{dd x,y;}p[maxn],O;
dd R;

dd getd(point a,point b){ return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));}
point getO(point p1,point p2,point p3)
{
    point res;
    dd a=p2.x-p1.x,b=p2.y-p1.y,c=p3.x-p2.x,d=p3.y-p2.y;
    dd e=sqr(p2.x)+sqr(p2.y)-sqr(p1.x)-sqr(p1.y);
    dd f=sqr(p3.x)+sqr(p3.y)-sqr(p2.x)-sqr(p2.y);
    res.x=(f*b-e*d)/(c*b-a*d)/2.0;
    res.y=(a*f-e*c)/(a*d-b*c)/2.0;
    return res;
}

void mincir()
{
    O=p[1]; R=0;
    for(int i=1;i<=n;++i)
    if(getd(p[i],O)-R>eps)
    {
        O=p[i]; R=0;
        for(int j=1;j<i;j++)
        if(getd(p[j],O)-R>eps)
        {
            O=(point){(p[i].x+p[j].x)/2.0,(p[i].y+p[j].y)/2.0};
            R=getd(p[i],p[j])/2.0;

            for(int k=1;k<j;++k)
            if(getd(p[k],O)-R>eps)
            {
                O=getO(p[i],p[j],p[k]);
                R=getd(p[i],O);
            }
        }
    }
}

int main()
{
    scanf("%d", &n);
    for(int i=1;i<=n;++i)
    scanf("%lf%lf",&p[i].x,&p[i].y);

    random_shuffle(p+1,p+1+n);

    mincir();
    printf("%.8f", R);
    return 0;
}