Problem:
Score : 200 points

Problem Statement

Given is a sequence of N integers A_1, \ldots, A_N.

Find the (multiplicative) inverse of the sum of the inverses of these numbers, \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.

Constraints

1 \leq N \leq 100

1 \leq A_i \leq 1000

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

Print a decimal number (or an integer) representing the value of \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.

Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.

Sample Input 1

2
10 30

Sample Output 1

7.5

\frac{1}{\frac{1}{10} + \frac{1}{30}} = \frac{1}{\frac{4}{30}} = \frac{30}{4} = 7.5.

Printing 7.50001, 7.49999, and so on will also be accepted.

Sample Input 2

3
200 200 200

Sample Output 2

66.66666666666667

\frac{1}{\frac{1}{200} + \frac{1}{200} + \frac{1}{200}} = \frac{1}{\frac{3}{200}} = \frac{200}{3} = 66.6666....

Printing 6.66666e+1 and so on will also be accepted.

Sample Input 3

1
1000

Sample Output 3

1000

\frac{1}{\frac{1}{1000}} = 1000.

Printing +1000.0 and so on will also be accepted.

Solution in Scala (2.13.1) (judge verdict: Wrong Answer)

import scala.annotation.tailrec

object Main extends App {

  @tailrec
  def gcd(x: Long, y: Long): Long = if (y == 0) x else gcd(y, x % y)

  def lcm(x: Long, y: Long): Long = if (x == 0 || y == 0) 0 else (x * y) / gcd(x, y)

  val sc = new java.util.Scanner(System.in)
  val x :: xs = List.fill(sc.nextInt())(sc.nextLong())
  val (numerator, denominator) = xs.foldLeft(1L -> x) {
    case ((count, l), r) =>
      val denominator = lcm(l, r)
      (count * (denominator / l) + (denominator / r)) -> denominator
  }
  println(1.0 / (numerator.toDouble / denominator))
}