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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.*

fun main(args:Array<String>){
    val n = readLine()!!.toInt()
    val x = DoubleArray(n)
    val y = DoubleArray(n)
    for(i in 0 until n){
        val (a,b) = readLine()!!.split(" ").map{it.toDouble()}
        x[i] = a
        y[i] = b
    }
    var ans = 1e18
    for(i in 0 until n) {
        for (j in i + 1 until n) {
            val midy = (y[i] + y[j]) / 2.0
            val midx = (x[i] + x[j]) / 2.0
            var ma = 0.0
            for(l in 0 until n){
                ma = Math.max(ma, Math.sqrt(Math.pow(x[l] - midx, 2.0) + Math.pow(y[l] - midy, 2.0)))
            }
            ans = Math.min(ans, ma)
        }
    }
    println("%.20f".format(ans))
}