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;
#define N 55
#define EPS 1e-10
#define db double
int n;db r;
struct Point
{
	db x,y;
	Point(db _x=0,db _y=0) {x=_x;y=_y;}
	Point operator + (Point t) {return Point(x+t.x,y+t.y);} 
	Point operator - (Point t) {return Point(x-t.x,y-t.y);}
	Point operator * (db t) {return Point(x*t,y*t);}
	Point operator / (db t) {return Point(x/t,y/t);}
}O,a[N];
db dst(Point x) {return sqrt(x.x*x.x+x.y*x.y);}
db crsMul(Point x,Point y) {return x.x*y.y-x.y*y.x;}
Point rot90(Point x) {return Point(x.y,-x.x);}
Point getI(Point x,Point y,Point z)
{
	Point M1,M2,v1,v2;M1=(x+y)/2;M2=(x+z)/2;v1=rot90(y-x);v2=rot90(z-x);
	return M1+v1*crsMul(M2-M1,v2)/crsMul(v1,v2);
}
int main()
{
	srand(time(0));scanf("%d",&n);
	for(int i=1;i<=n;++i) scanf("%lf %lf",&a[i].x,&a[i].y);
	random_shuffle(a+1,a+n+1);
	for(int i=1;i<=n;++i) if(dst(O-a[i])>r+EPS)
	{
		O=a[i];r=0;
		for(int j=1;j<i;++j) if(dst(O-a[j])>r+EPS)
		{
			O=(a[i]+a[j])/2;r=dst(O-a[j]);
			for(int k=1;k<j;++k) if(dst(O-a[k])>r+EPS)
				O=getI(a[i],a[j],a[k]),r=dst(O-a[k]);
		} 
	}printf("%.10lf\n",r);return 0;
}