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;
typedef long long ll;
typedef pair<int,int> P;

double x[100],y[100];
int N;
double mag = 10;
double memo[205][205];
double x_max = 1000;
double y_max = 1000;
double x_min = 0;
double y_min = 0;

double search(double cx, double cy){
    double ret = 0;
    for (int i = 0;i < N;i++){
        double dist = (cx-x[i])*(cx-x[i])+(cy-y[i])*(cy-y[i]);
        ret = max(ret,dist);
    }
    return ret;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    cin >> N;
    for (int i = 0;i < N;i++){
        cin >> x[i] >> y[i];
    }

    for (int pre= 0;pre < 1500;pre++){
        double m = 1e10;
        int ni,nj;
        for (int i = 0;i <= 100;i++){
            for (int j = 0;j <= 100;j++){
                memo[i][j] = search(x_min+i*mag, y_min+j*mag);
                if(memo[i][j] < m){
                    m = memo[i][j];
                    ni = i; nj = j;
                }
            }
        }
        x_min = x_min+(ni)*mag - mag*0.5*50;
        y_min = y_min+(nj)*mag - mag*0.5*50;
        mag *= 0.5;
    }

    printf("%.30f\n",sqrt(search(x_min+mag*50,y_min+mag*50)));

    return 0;

}