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: Wrong Answer)

fun main(args: Array<String>)
{
    val n = readInt()
    val a = readNInts()

    val prod = mutableListOf<Double>()
    for (i in 1..n) {
        var tmp = 1.0
        for (excluded in 1..n) {
            tmp *= if (i == excluded) 1.0 else a[i-1].toDouble()
        }
        prod.add(tmp)
    }
    var allProd = 1.0
    for (item in a) {
        allProd *= item.toDouble()
    }

    var sum = 0.0
    for (item in prod) {
        sum += item
    }

    println(allProd/sum)

}


// Read an integer
// Usage: val a = readInt()
private fun readInt() = readLine()!!.toInt()

// Read N integers separated by " "
// Usage: val (a, b, c) = readNInts()
private fun readNInts() = readLine()!!.split(" ").map(String::toInt)

// Read a string
// Usage: val a = readString()
private fun readString() = readLine()!!