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; 
typedef long long ll;
typedef long double ld;
#define pb push_back
#define fi first
#define se second
const ll mod = 1e9+7;
const int N = 2e5+6;
ld px[N],py[N];
int n;
ld chxy(ld x,ld y){
	ld ret = 0;
	for(int i=1;i<=n;i++){
		ret = max(ret,hypot(px[i]-x,py[i]-y));
	}
	return ret;
}
ld chy(ld x){
	ld st = 0;
	ld en = 1e4;
	for(int i=0;i<100;i++){
		ld len = (en-st)/3;
		ld mid1 = st+len;
		ld mid2 = en-len;
		if(chxy(x,mid1)<chxy(x,mid2)){
			en = mid2;
		}
		else{
			st = mid1;
		}
	}
	return min({chxy(x,st),chxy(x,en)});
}
ld ch(){
	ld st = 0;
	ld en = 1e4;
	for(int i=0;i<100;i++){
		
		ld len = (en-st)/3;
		ld mid1 = st+len;
		ld mid2 = en-len;
		if(chy(mid1)<chy(mid2)){
			en = mid2;
		}
		else{
			st = mid1;
		}
	}
	return min({chy(st),chy(en)});
}
void solve(){
	cout<<fixed<<setprecision(12);
	cin>>n; 
	for(int i=1;i<=n;i++)cin>>px[i]>>py[i];
	cout<<ch()<<endl;

}
int main(){
	ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	int t=1; 
//	cin>>t; 
	while(t--){
		solve();
	}
	return 0;
}