Problem:
Score : 600 points

Problem Statement

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}.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (ll i = (a); i < (b); i++)
#define rep2(r, aa, bb) for (ll r = (aa)-1; r >= (bb); r--)
#define be(x) (x.begin(), x.end())
#define pb(t) push_back(t)
#define ll long long
#define mp(a, b) make_pair(a, b)
struct P{
	long double x, y;
	void read(){
		cin>>x>>y;
	}
	int operator *(P b){
		return x*b.y-y*b.x;
	}
	P operator -(P b){
		return {x-b.x, y- b.y};
	}
	double slope(P b){
		return (double)(b.y-y)/(b.x-x);
	}
	long double dist(P b){
		return sqrt((y- b.y)*(y- b.y)+(x-b.x)*(x-b.x));
	}
	bool operator <(P b){
		if(x!=b.x)return x<b.x;
		return y<b.y;
	}
};
int main(){
	ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    cout<<fixed<<setprecision(20);
    ll n;
    cin>>n;
    vector<P>A(n);
    rep(i,0,n)
		A[i].read();
	long double mini=LLONG_MIN;
	rep(i,0, n){
		rep(j,i+1, n){
		mini=max(mini, A[i].dist(A[j]));
	}
	}
	cout<<mini/2.0<<"\n";
}