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>
#define N 1010
using namespace std;
int n;
double ansx,ansy,ans;
double totx=0,toty=0;
double t;
double delta=0.999;
struct node{
	double x,y,w;
};node f[N];
double check(double x,double y) {
	double dx,dy,ret=0;
	for(int i=1;i<=n;i++) {
		dx=x-f[i].x;
		dy=y-f[i].y;
		ret=max(sqrt(dx*dx+dy*dy),ret);
	}
	return ret;
}
void sa() {
	t=45000;
	while(t>1e-18) {
		double tx=ansx+(rand()*2-RAND_MAX)*t;
		double ty=ansy+(rand()*2-RAND_MAX)*t;
		double a=check(tx,ty);
		double an=a-ans;
//		printf("%lf %lf %lf\n",tx,ty,a);
		if(an<0) ansx=tx,ansy=ty,ans=a;
		else if(exp(-an/t)*RAND_MAX>rand()) ansx=tx,ansy=ty;
		t*=delta;
	}
}
int main() {
	srand(1960);
	scanf("%d",&n);
	for(int i=1;i<=n;i++) {
		cin>>f[i].x>>f[i].y;
		totx+=f[i].x;
		toty+=f[i].y; 
	}
	ansx=totx/n;
	ansy=toty/n;
	ans=check(ansx,ansy);
	for(int i=1;i<=10;i++) sa();
	double dx,dy,ret;
	for(int i=1;i<=n;i++) {
		dx=ansx-f[i].x;
		dy=ansy-f[i].y;
		ret=max(sqrt(dx*dx+dy*dy),ret);
	}
	cout<<fixed<<setprecision(7)<<ret;
	return 0;
}