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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <string>
#include <vector>
#include <set>
#include <bits/stdc++.h>
#include <iomanip>
#include <numeric>
#include <utility>
#include <map>
#include <algorithm>
typedef long long ll;
using namespace std;
#define MX 1000000000

long long GCD(long long a, long long b)
{
    if (b > a)
        swap(a, b);
    if (a % b == 0)
        return b;
    return GCD(b, a % b);
}
long long LCM(long long a, long long b)
{
    return a * b / GCD(a, b);
}
int main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll N, lcm = 1;
    cin >> N;
    vector<ll> vec(N);
    for (int i = 0; i < N; ++i)
        cin >> vec[i];
    ll bunshi = 1;
    ll bunbo = vec[0];
    for (ll i = 1; i < N; ++i)
    {
        bunshi = vec[i] * bunshi + bunbo;
        bunbo *= vec[i];
    }
    cout << fixed << setprecision(15); 
    cout << double(bunbo) / bunshi << "\n";
}