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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            ulong N = ulong.Parse(Console.ReadLine());
            var input = Console.ReadLine().Split(' ').Select(x => ulong.Parse(x)).ToArray();

            ulong a = 1;
            for (ulong i = 0; i < N - 1; i++)
            {
                ulong tmp = Lcm(input[i], input[i + 1]);

                a = (tmp / input[i]) * a + tmp / input[i + 1];
                input[i + 1] = tmp;
            }

            Console.WriteLine((double)input[N - 1] / a);

        }

        static ulong Gcd(ulong m, ulong n)
        {
            ulong temp;
            while (m % n != 0)
            {
                temp = n;
                n = m % n;
                m = temp;
            }
            return n;
        }

        static ulong Lcm(ulong m, ulong n)
        {
            return m * n / Gcd(m, n);
        }
    }
}