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;

vector<pair<double,double>> pr;


double dist(pair<double,double> p, pair<double,double> q){
    double x = p.first - q.first;
    double y = p.second - q.second;
    return sqrt(x*x + y*y);
}

double f(double x,double y){
    double res = 0;
    for(int i = 0; i < (int)pr.size(); i++){
        res = max(res, dist({x,y},pr[i]));
    }
    return res;
}

double g(double x){
    double l = 0,r = 1000;
    for(int i = 0; i < 80; i++){
        double y1 = (l*2+r)/3;
        double y2 = (l+r*2)/3;
        if(f(x,y1)>f(x,y2)) l = y1; else r = y2;
    }
    return f(x,l);
}


int main(){
    int n;cin>>n;
    for(int i = 0; i < n; i++){
        double x,y;cin>>x>>y;
        pr.push_back({x,y});
    }
    double l = 0, r = 1000;
    for(int i = 0; i < 80; i++){
        double x1 = (l*2+r)/3;
        double x2 = (l+r*2)/3;
    if(g(x1)>g(x2)) l = x1; else r = x2;
    }

    double res = g(l);
    cout<<fixed<<setprecision(12)<<res;
    
}