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.io.InputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	InputStream in = System.in;
	PrintStream out = System.out;

	double d(int a, int b) {
		return Math.sqrt(Math.pow(x[a] - x[b], 2) + Math.pow(y[a] - y[b], 2));
	}

	int N;
	int[] x, y;

	public void _main(String[] args) {
		Scanner sc = new Scanner(in);

		N = sc.nextInt();
		x = new int[N];
		y = new int[N];

		for (int i = 0; i < N; i++) {
			x[i] = sc.nextInt();
			y[i] = sc.nextInt();
		}

		sc.close();

		double ans = Double.MIN_VALUE;

		for (int i = 0; i < N; i++) {
			for (int j = i + 1; j < N; j++) {
				ans = Math.max(ans, d(i, j));
			}
		}

		out.println(ans / 2);

	}

	public static void main(String[] args) {
		new Main()._main(args);
	}
}