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;

using ll = long long;
const long long MOD = 1e9+7;

int main() {
    int n;
    cin >> n;
    vector<double> x(n), y(n);
    for (int i = 0; i < n; i++) {
        cin >> x.at(i) >> y.at(i);
    }

    double rate = 1.0;
    int LOOP = 1000000;
    double cx = 0, cy = 0;
    for (int l = 0; l < LOOP; l++) {
        double max_d = 0.0;
        double max_x = 0, max_y = 0;
        for (int i = 0; i < n; i++) {
            double dx = cx - x.at(i), dy = cy - y.at(i);
            double d = sqrt(dx * dx + dy * dy);
            if (max_d < d) {
                max_d = d;
                max_x = x.at(i);
                max_y = y.at(i);
            }
        }
        cx += (max_x - cx) * rate;
        cy += (max_y - cy) * rate;

        rate *= 0.999;
    }
    
    double max_d = 0;
    for (int i = 0; i < n; i++) {
        double dx = cx - x.at(i), dy = cy - y.at(i);
        double d = sqrt(dx * dx + dy * dy);
        max_d = max(max_d, d);
    }
    printf("%.10lf\n", max_d);
}