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.BufferedReader;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		int[] x = new int[n];
		int[] y = new int[n];
		for (int i = 0; i < n; i++) {
			sa = br.readLine().split(" ");
			x[i] = Integer.parseInt(sa[0]);
			y[i] = Integer.parseInt(sa[1]);
		}
		br.close();

		double ans = 100000;
		int mi = 0;
		int mj = 0;
		for (int i = 0; i < n; i++) {
			for (int j = i + 1; j < n; j++) {
				double mx = (x[i] + x[j]) / 2.0;
				double my = (y[i] + y[j]) / 2.0;
				double ng = 0;
				double ok = 100000;
				while (Math.abs(ok - ng) > 1e-8) {
					double mid = (ok + ng) / 2;
					if (isOk(x, y, mx, my, mid)) {
						ok = mid;
					} else {
						ng = mid;
					}
				}
				ans = Math.min(ans, ok);
			}
		}
		System.out.println(ans);
	}

	static boolean isOk(int[] x, int[] y, double mx, double my, double val) {
		for (int i = 0; i < y.length; i++) {
			double d = Math.hypot(x[i] - mx, y[i] - my);
			if (d > val) {
				return false;
			}
		}
		return true;
	}
}