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 (1.0.0) (judge verdict: Accepted)

import java.util.*

fun main(args: Array<String>) {
    val scanner = Scanner(System.`in`)
    val n = scanner.nextInt()
    val array = Array(n, {0.0})
    for(i in 0..n-1){
        array[i] = scanner.nextDouble()
    }
    var gcd = array[0]
    for(i in 1..n-1){
        gcd = gcd * array[i] / cal(gcd, array[i])
    }
    var sum = 0.0
    for(i in 0..n-1){
        sum += gcd / array[i]
    }
    println(gcd / sum)
}

fun cal(x:Double, y:Double): Double{
    var x2 = x;
    var y2 = y;
    if(x2 < y2) return cal(y2, x2);
    if(y2 === 0.0) return x2;
    return cal(y2, x2 % y2);
}