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.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.io.PrintWriter
import java.lang.StringBuilder
import java.util.*

fun PrintWriter.solve(sc: FastScanner) {
    val n = sc.nextInt()
    val pos = Array(n) { sc.nextInt().toDouble() to sc.nextInt().toDouble() }
    var min = Double.MAX_VALUE
    for (i in 0 until n) {
        for (j in i + 1 until n) {
            for (k in j + 1 until n) {
                val (x1,y1) = pos[i]
                val (x2,y2) = pos[j]
                val (x3,y3) = pos[k]
                val ox=((y2-y1)*((y3*y3-y1*y1)+(x3*x3-x1*x1))-(y3-y1)*((y2*y2-y1*y1)+(x2*x2-x1*x1)))/
                        (2*((x3-x1)*(y2-y1)-(x2-x1)*(y3-y1)))
                val oy = if(y2 != y1){
                    (2*(x1-x2)*ox+(y2*y2-y1*y1)+(x2*x2-x1*x1))/(2*(y2-y1))
                }else{
                    (2*(x1-x3)*ox+(y3*y3-y1*y1)+(x3*x3-x1*x1))/(2*(y3-y1))
                }

                val r = Math.sqrt((ox-x1)*(ox-x1)+(oy-y1)*(oy-y1));
                var ok = true
                for (k in 0 until n) {
                    val (x,y) = pos[k]
                    val d = Math.sqrt((ox-x)*(ox-x)+(oy-y)*(oy-y))
                    if (d > r) {
                        ok = false
                        break
                    }
                }
                if (ok) {
                    min = Math.min(min, r)
                }
            }
        }
    }
    for (i in 0 until n) {
        for (j in i+1 until n) {
            val (x1,y1) = pos[i]
            val (x2,y2) = pos[j]
            val (ox, oy) = (x1+x2)/2 to (y1+y2)/2
            val r = Math.sqrt((ox-x1)*(ox-x1)+(oy-y1)*(oy-y1));
            var ok = true
            for (k in 0 until n) {
                val (x,y) = pos[k]
                val d = Math.sqrt((ox-x)*(ox-x)+(oy-y)*(oy-y))
                if (d > r) {
                    ok = false
                    break
                }
            }
            if (ok) {
                min = Math.min(min, r)
            }
        }
    }
    println(min)
}

fun main(args: Array<String>) {
    val writer = PrintWriter(System.out, false)
    writer.solve(FastScanner(System.`in`))
    writer.flush()
}

class FastScanner(s: InputStream) {
    private var st = StringTokenizer("")
    private val br = BufferedReader(InputStreamReader(s))

    fun next(): String {
        while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())

        return st.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextLine() = br.readLine()
    fun nextDouble() = next().toDouble()
    fun ready() = br.ready()
}