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<algorithm>
#include<cmath>
#include<cstdio>
using namespace std;

int n;
int x[1000], y[1000];

int main() {
    scanf("%d", &n);
    for (int i = 0; i < n; i++) scanf("%d %d", &x[i], &y[i]);
    
    if (n == 2) {
        printf("%5.15lf\n", hypot(x[1] - x[0], y[1] - y[0]) / 2);
        return 0;
    }
    double ans = 0.0;
    for (int i = 0; i < n - 2; i++) {
        for (int j = i + 1; j < n - 1; j++) {
            for (int k = j + 1; k < n; k++) {
                int d[3];
                d[0] = (x[j] - x[i]) * (x[j] - x[i]) + (y[j] - y[i]) * (y[j] - y[i]);
                d[1] = (x[k] - x[j]) * (x[k] - x[j]) + (y[k] - y[j]) * (y[k] - y[j]);
                d[2] = (x[i] - x[k]) * (x[i] - x[k]) + (y[i] - y[k]) * (y[i] - y[k]);
                sort(d, d + 3);
                if (d[2] >= d[0] + d[1]) {
                    ans = max(ans, sqrt(d[2]) / 2);
                    continue;
                }
                double s = sqrt(1.0 - static_cast<double>(d[0] + d[1] - d[2]) *
                           (d[0] + d[1] - d[2]) / 4 / d[0] / d[1]);
                ans = max(ans, sqrt(d[2]) / s / 2);
            }
        }
    }

    printf("%5.15lf\n", ans);
    return 0;
}