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;

public class Main {

	public static void main(String[] args) 
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		double minx = 0;
		double miny = 0;
		double maxx = 0;
		double maxy = 0;
		double[] ax = new double[n];
		double[] ay = new double[n];
		for(int i = 0; i < n; i++)
		{
			double x = sc.nextDouble();
			double y = sc.nextDouble();
			ax[i]=x;
			ay[i]=y;
			if(i == 0)
			{
				minx = x;
				miny = y;
				maxx = x;
				maxy = y;
			}
			else
			{
				minx = Math.min(minx, x);
				miny = Math.min(miny, y);
				maxx = Math.max(maxx, x);
				maxy = Math.max(maxy, y);
			}
		}
		
		double x = ((double)maxx + (double)minx)/2;
		double y = ((double)maxy + (double)miny)/2;
		double d = 0;
		for(int i = 0; i < n; i++)
		{
			double dif = Math.sqrt((x-ax[i])*(x-ax[i]) + (y-ay[i])*(y-ay[i]));
			d = Math.max(dif, d);
		}
		System.out.println(d);
	}

}