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:
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define pp pair<int,int>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define ld long double
#define al(a) (a).begin(),(a).end()
#define mk make_pair
#define check cout<<"?"<<endl;

ll MOD=1000000007;
ll mod=998244353;
int inf=1000001000;
ll INF=1e18+5;

ll n;
vector<pair<ll,ll>> p;

ld max_d(ld x,ld y){
    ld res=-1;
    rep(i,n) 
    res=max(res,(x-p[i].first)*(x-p[i].first)+(y-p[i].second)*(y-p[i].second));
    return res;
}

ld f(ld x){
    ld l=-1000000,r=1000000;
    ld tl,tr;
    rep(_,160){
        tl=(2*l+r)/3;
        tr=(l+2*r)/3;
        if(max_d(x,tl)>=max_d(x,tr)) l=tl;
        else r=tr;
    }
    return max_d(x,l);
}

int main(){
    cout<<fixed<<setprecision(15);
    cin>>n;
    p.assign(n,mk(0,0));
    rep(i,n){
        ll x,y; cin>>x>>y;
        p[i]=mk(x,y);
    }
    ld l=-1000000,r=1000000;
    ld tl,tr;
    rep(_,160){
        tl=(2*l+r)/3;
        tr=(l+2*r)/3;
        if(f(tl)>=f(tr)) l=tl;
        else r=tr;
    }
    cout<<sqrt(f(l))<<endl;
}