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;
#define ll long long int
#define MOD 1000000007
long double dist(long double a,long double b) {
	return a*a + b*b;
}
int main()
{  ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    ll n;
    cin>>n;
    long double x[n],y[n];
    long double X=0,Y=0;
	for (int i = 0; i < n; i++) {
		cin>>x[i]>>y[i];
		X+=x[i];Y+=y[i];
	}
	X/=n; Y/=n;
	long double P=0.1,e,d;
	for (int i = 0;i< 30000; i++) {
		ll f = 0;
		d=dist(X- x[0],Y-y[0]);
		for (int j=1;j<n;j++) {
			e = dist(X-x[j],Y-y[j]);
			if (d<e) {d= e; f = j; }
		}
		X += (x[f] - X)*P;
		Y += (y[f] - Y)*P;
		P *= 0.999;
	}
	cout<<fixed;
	cout<<setprecision(10)<<sqrt(d);
}