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)

internal data class Dot(
    val x: Int,
    val y: Int
) {
    fun getDistance(other: Dot): Double {
        return Math.sqrt(Math.pow((this.x - other.x).toDouble(), 2.0) + Math.pow((this.y - other.y).toDouble(), 2.0))
    }
}

internal fun solve(count: Int, dots: List<Dot>): String {
    return (dots.subList(0, count - 1).mapIndexed { index, dot ->
        {
            dots.subList(index + 1, count).map { dot.getDistance(it) }.max()!!
        }
    }.map { it() }.max()?.div(2)).toString()
}

fun main(args: Array<String>) {
    var OUTPUT = ""

    val br = System.`in`.bufferedReader()
    val count = br.readLine().toInt()
    val dots = mutableListOf<Dot>()
    repeat(count) { dots.add(br.readLine().split(" ").map { it.toInt() }.let { Dot(it[0], it[1]) }) }

    OUTPUT += solve(count, dots)
    print(OUTPUT)
}