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:
#define HAVE_STRUCT_TIMESPEC
#include<bits/stdc++.h>
using namespace std;
double x[1007],y[1007];
double X,Y,d,e,P=0.1;
int main(){
    int n;
	scanf("%d",&n);
	for(int i=0;i<n;++i){
		scanf("%lf%lf",&x[i],&y[i]);
		X+=x[i];
		Y+=y[i];
	}
	X/=n;
	Y/=n;
	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){
			e=(X-x[j])*(X-x[j])+(Y-y[j])*(Y-y[j]);
			if(d<e)
                d=e,f=j;
		}
		X+=(x[f]-X)*P;
		Y+=(y[f]-Y)*P;
		P*=0.999;
	}
	printf("%.10lf",sqrt(d));
}