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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
class Main{
  public static void main(String[] args){
    Scanner scn = new Scanner(System.in);
    String[] str = scn.nextLine().split(" ");
    int n = Integer.parseInt(str[0]);
    int max=0,x,y;
    String[] tmp;
    for(int i=0;i<n;i++){
      tmp = scn.nextLine().split(" ");
      x=Integer.parseInt(tmp[0]);
      x*=x;
      y=Integer.parseInt(tmp[1]);
      y*=y;
      if(x+y>max) max=x+y;
    }
    System.out.println(Math.sqrt(max)/2);
  }
}