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

int main(){
	int n;
	scanf("%d", &n);
	vector<double> x(n), y(n);
	for(int i = 0; i < n; ++i){
		scanf("%lf%lf", &x[i], &y[i]);
	}
	double ratio = 0.5;
	double px = 0, py = 0, mr = 0;
	while(ratio > 1e-12){
		for(int t = 0; t < 50; ++t){
			mr = 0;
			int k = 0;
			for(int i = 0; i < n; ++i){
				double d = hypot(px - x[i], py - y[i]);
				if(mr < d){
					mr = d;
					k = i;
				}
			}
			px += ratio * (x[k] - px);
			py += ratio * (y[k] - py);
		}
		ratio /= 1.4;
	}
	printf("%.9f\n", mr);
}