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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class Program
{
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine().Trim());

        List<int> lx = new List<int>();
        List<int> ly = new List<int>();

        for (int i = 0; i < n; i++)
        {
            string[] l = Console.ReadLine().Split(' ');
            int x = int.Parse(l[0]);
            lx.Add(x);
            int y = int.Parse(l[1]);
            ly.Add(y);
        }
        int lenx = lx.Max() - lx.Min();
        int leny = ly.Max() - ly.Min();
        double leng = Math.Sqrt(lenx * lenx + leny * leny);

        Console.WriteLine((leng / 2.0).ToString());

        Console.ReadKey();
    }
}