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>
using namespace std;

int n, m=20000, mi;
double cx, cy, d, mx, p=1.0, x[55], y[55];
double f(double p, double q) {return p*p + q*q;}

int main() {
	int i;
	cin >> n;
	for(i=0; i<n; i++) {
		cin >> x[i] >> y[i];
		cx += x[i]; cy += y[i];
	}
	cx /= n; cy /= n;
	while(m--) {
		mx = f(cx - x[0], cy - y[0]);
		mi = 0;
		for(i=1; i<n; i++) {
			d = f(cx - x[i], cy - y[i]);
			if(d > mx) mx = d, mi = i;
		}
		cx += (x[mi] - cx) * p;
		cy += (y[mi] - cy) * p;
		p *= 0.999;
	}
	printf("%.9f", sqrt(mx));
	return 0;
}