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 <iostream>
#include <cmath>
using namespace std;


int main(void){
    // Your code here!
    int a[50],b[50];
    int n;
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>a[i]>>b[i];
    }
    double xx=500,yy=500;
    double d=300;
    double max=0;
    while(true){
        max=0;
        double maxx,maxy;
        for(int i=0;i<n;i++){
            double tmp=(xx-a[i])*(xx-a[i])+(yy-b[i])*(yy-b[i]);
            if(tmp>max){
                max=tmp;maxx=a[i];maxy=b[i];
            }
        }
        double dtmp=sqrt(max);
        
        xx+=d*(maxx-xx)/dtmp;
        yy+=d*(maxy-yy)/dtmp;
        d/=1.03;
        if(d<0.00000001)break;
    }
    cout<<sqrt(max)<<endl;
    return 0;
}