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;

const int N = 50;

pair<double,double> dat[N+5];

int main() {
    pair<double,double> summ = make_pair((double)0.0, (double)0.0);

    int n; scanf("%d", &n);
    for (int i=1; i<=n; i++) {
        scanf("%lf %lf", &dat[i].first, &dat[i].second);
        summ.first += dat[i].first;
        summ.second += dat[i].second;
    }
    summ.first /= (double)n;
    summ.second /= (double)n;

    double res = (double)0.0;
    double P = (double)1.0;

    for (int xxx=0; xxx<300000; xxx++) {
        int f = 1;
        res = hypot(summ.first - dat[1].first, summ.second - dat[1].second);

        for (int i=1; i<=n; i++) {
            double ret = hypot(summ.first - dat[i].first, summ.second - dat[i].second);
            if (res < ret) res = ret, f = i;
        }

        summ.first += (dat[f].first - summ.first)*P;
        summ.second += (dat[f].second - summ.second)*P;
        P *= 0.999;
    }

    printf("%.8lf\n", res);
    return 0;
}