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 double long double
using namespace std;
struct node{
    double x,y;
}a[105];
int n;
double ansx,ansy,sy=0,sx=0;
double ans=2000,t;
double del=0.9995; 
inline double dis(node aa,node bb){
    return sqrt((aa.x-bb.x)*(aa.x-bb.x)+(aa.y-bb.y)*(aa.y-bb.y));
}
double calc(double x,double y){
    double ans=0;
    for(int i=1;i<=n;i++){
        ans=max(ans,dis((node){x,y},a[i]));
    }
    return ans;
}
void SA(){
    double x=ansx,y=ansy;
    t=2000;
    while(t>1e-14){
        double X=x+((rand()<<1)-RAND_MAX)*t;
        double Y=y+((rand()<<1)-RAND_MAX)*t;
        double now=calc(X,Y);
        double Delta=now-ans;
        if(Delta<0){
            x=X,y=Y;
            ans=now;
        }
        else if (exp(-Delta/t)*RAND_MAX>rand()) x=X,y=Y;
        t*=del;
    }
}
int main(){
    int cnt=0;
    srand(1000211237);
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        cin>>a[i].x>>a[i].y;
        sx+=a[i].x,sy+=a[i].y;
    }
    ansx=(double)sx/n,ansy=(double)sy/n;
    while((double)clock()/CLOCKS_PER_SEC<0.93) SA(),cnt++;
    printf("%.14Lf",ans);
    return 0;
}