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: Accepted)

fun main(args: Array<String>) {
    val N = readLine()!!.toInt()
    val p = Array(N) {
        val (x, y) = readLine()!!.split(" ").map{it.toDouble()}
        Pair(x, y)
    }

    fun dot(a: Pair<Double, Double>, b: Pair<Double, Double>): Double {
        return a.first * b.first + a.second * b.second
    }
    fun cross(a: Pair<Double, Double>, b: Pair<Double, Double>): Double {
        return a.first * b.second - a.second * b.first
    }

    fun plus(a: Pair<Double, Double>, b: Pair<Double, Double>): Pair<Double, Double> {
        return Pair(a.first + b.first, a.second + b.second)
    }

    fun minus(a: Pair<Double, Double>, b: Pair<Double, Double>): Pair<Double, Double> {
        return Pair(a.first - b.first, a.second - b.second)
    }

    fun dist(x: Double, y: Double, p: Pair<Double, Double>): Double {
        return Math.sqrt(Math.pow(p.first - x, 2.0) + Math.pow(p.second - y, 2.0))
    }

    var cx = 0.0
    var cy = 0.0
    var alpha = 0.7
    var r = 1e18

    for (k in 1..100000) {
        var t = -1
        var mr = 0.0

        for (i in p.indices) {
            val d = dist(cx, cy, p[i])
            if (d > mr) {
                mr = d
                t = i
            }
        }

        val v = minus(p[t], Pair(cx, cy))
        cx += v.first * alpha
        cy += v.second * alpha

        alpha *= 0.999
        r = mr
    }

    System.out.printf("%1.10f\n", r)
}