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 <cstdio>
#include <cmath>
#define N 55
using namespace std;

int T = 5e5;
double n, tx, ty, p = 1, pr = 0.999, mx, t, x[N], y[N];
int main()
{
	int i, j, num;
	cin >> n;
	for (i =0; i < n; i++) {
		cin >> x[i] >> y[i];
		tx += x[i];
		ty += y[i];
	}
	tx /= (double)n;
	ty /= (double)n;
	while (T--) {
		mx = -1;
		for (i = 0; i < n; i++) {
			t = (x[i] - tx) * (x[i] - tx) + (y[i] - ty) * (y[i] - ty);
			if (t > mx) {
				mx = t;
				num = i;
			}
		}
		p *= pr;
		tx = (x[num] - tx) * p + tx;
		ty = (y[num] - ty) * p + ty;
	}
	printf("%.10f", sqrt(mx));
    return 0;
}