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: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author varunvats32
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        FEncloseAll solver = new FEncloseAll();
        solver.solve(1, in, out);
        out.close();
    }

    static class FEncloseAll {
        static int n;
        static int[] x;
        static int[] y;

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            n = in.nextInt();
            x = new int[n];
            y = new int[n];

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

            double l = 0, r = 1000;
            for (int i = 1; i <= 80; i++) {
                double m1 = l + (r - l) / 3;
                double m2 = r - (r - l) / 3;
                if (g(m1) > g(m2))
                    l = m1;
                else r = m2;
            }

            double ans = g(l);
            out.printf("%.10f\n", ans);
        }

        double g(double x) {
            double l = 0, r = 1000;
            for (int i = 1; i <= 80; i++) {
                double m1 = l + (r - l) / 3;
                double m2 = r - (r - l) / 3;
                if (f(x, m1) > f(x, m2))
                    l = m1;
                else r = m2;
            }

            return f(x, l);
        }

        double f(double x1, double y1) {
            double res = 0;
            for (int i = 0; i < n; i++) {
                res = Math.max(res, dist(x[i], y[i], x1, y1));
            }
            return res;
        }

        double dist(double x1, double y1, double x2, double y2) {
            double dx = x1 - x2;
            double dy = y1 - y2;

            return Math.sqrt(dx * dx + dy * dy);
        }

    }
}