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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
using namespace std;
#define rep(i,n) for(int i = 0;i<n;i++)
const long long MOD = 1000000007LL;
const string alpha = "abcdefghijklmnopqrstuvwxyz";
long double dist(long double center[],long double p[]){
    long double l = 0;
    rep(i,2) l+=((center[i]-p[i])*(center[i]-p[i]));
    return sqrt(l);
}
int main(){  
    int n;
    cin >> n;
    long double point[n][2];
    rep(i,n) cin >> point[i][0] >> point[i][1];
    long double move = 0.5;
    long double center[2] = {0.0,0.0};
    while(move>1e-8){
        rep(j,100){
            long double maxl = 0;
            int maxk = 0;
            rep(i,n){
                long double d = dist(center,point[i]);
                if(d>maxl){
                    maxk = i;
                    maxl = d;
                }
            }    
            rep(i,2) center[i]+=((point[maxk][i]-center[i])*move);        
        }
        move/=2;
    }
    long double ans = 0;
    rep(i,n) ans = max(ans,dist(center,point[i]));
    cout << setprecision(20) << ans << endl;
}