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 implements Runnable {

    private static int MOD = 1_000_000_007;

    public static void main(String[] args) {
        // Run with 32MB stack
        Thread thread = new Thread(null, new Main(), "", 32 * 1024 * 1024);
        thread.start();
    }

    @Override
    public void run() {
        final Scanner scanner = new Scanner(System.in);
        solve(scanner);
    }

    static void solve(Scanner scanner) {
        int N = Integer.parseInt(scanner.next());
        int[][] A = new int[N][2];
        for (int i = 0; i < N; i++) {
            A[i][0] = Integer.parseInt(scanner.next());
            A[i][1] = Integer.parseInt(scanner.next());
        }

        double x = 0, y = 0;
        for (int i = 0; i < N; i++) {
            x += A[i][0];
            y += A[i][1];
        }
        x /= N;
        y /= N;

        double temp = 0.1;
        double max = 0;
        for (int i = 0; i < 3_000_000; i++) {
            double xto = 0, yto = 0;
            max = 0;
            for (int j = 0; j < N; j++) {
                double x2 = A[j][0], y2 = A[j][1];
                double diff = Math.sqrt((x2 - x) * (x2 - x) + (y2 - y) * (y2 - y));
                if (diff > max) {
                    max = diff;
                    xto = x2;
                    yto = y2;
                }
            }

            double ydiff = yto - y;
            double xdiff = xto - x;
            double dy = temp * (ydiff * ydiff / (xdiff * xdiff + ydiff * ydiff));
            double dx = temp * (xdiff * xdiff / (xdiff * xdiff + ydiff * ydiff));
            if (xdiff > 0) {
                x += dx;
            } else {
                x -= dx;
            }
            if (ydiff > 0) {
                y += dy;
            } else {
                y -= dy;
            }
            temp *= 0.99999;
        }

        System.out.println(max);
    }
}