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 (2.11.7) (judge verdict: Accepted)

object Main extends App {

  //最大公約数
  def gcd(x: Long, y: Long): Long = {
    if(y == 0) x
    else gcd(y, (x % y))
  }

  //最小公倍数
  def lcm(x: Long, y: Long): Long = {
    if(x == 0 || y == 0) 0
    else (x * y) / gcd(x, y)
  }

  val n = scala.io.StdIn.readInt()
  val readA =  scala.io.StdIn.readLine()
  val aArray = readA.split(" ").map(_.toLong).toVector
  var kobaisuu = 1L

  aArray.foreach(a =>
    kobaisuu = lcm(a, kobaisuu)
  )
  val bunshiArray = aArray.map(a => kobaisuu / a)
  println(kobaisuu.toDouble / bunshiArray.sum.toDouble)
}