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 Kotlin (1.3.71) (judge verdict: Accepted)

fun main() {
  val N = readInt()
  val A = readInts()
  println(1.0 / A.map { 1.0 / it }.sum())
}

fun gcd(a: Int, b: Int): Int = if (a < b) gcd(b, a) else if (b == 0) a else gcd(b, a % b)
fun gcd(a: Long, b: Long): Long = if (a < b) gcd(b, a) else if (b == 0L) a else gcd(b, a % b)
fun lcm(a: Int, b: Int): Int = (a * b) / gcd(a, b)
fun lcm(a: Long, b: Long): Long = (a * b) / gcd(a, b)

fun readString() = readLine()!!
fun readStrings() = readLine()!!.split(" ")
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readInts() = readLine()!!.split(" ").map { it.toInt() }
fun readLongs() = readLine()!!.split(" ").map { it.toLong() }