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.*;

public class Main{
  public static void main(String[]args){
    Scanner sc = new Scanner(System.in);
    int N = Integer.parseInt(sc.nextLine());
    int[][] val = new int[N][2];
    for(int i = 0; i < N; i++){
      String[] S = sc.nextLine().split(" ");
      val[i][0] = Integer.parseInt(S[0]);
      val[i][1] = Integer.parseInt(S[1]);
    }
    double max = 0.0;
    for(int i = 0; i < N-1; i++){
      for(int j = i+1; j < N; j++){
        double A = Math.pow(val[j][0]-val[i][0], 2);
        double B = Math.pow(val[j][1]-val[i][1], 2);
        double D = Math.sqrt(A+B);
        if(max < D){
          max = D;
        }
      }
    }
    System.out.println(max/2);
  }
}