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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::stdin;

fn main(){
    let mut n = String::new();
    stdin().read_line(&mut n).unwrap();
    let n: usize = n.trim().parse().unwrap();

    let mut a = String::new();
    stdin().read_line(&mut a).unwrap();
    let a: Vec<usize> = a.trim().split_whitespace().flat_map(str::parse).collect();

    let mut den = 1;
    let mut num = 0;
    for i in 0..n {
        let mut b = 1;
        for j in 1..n {
            b *= a[(i + j) % n];
        }
        num += b;
        den *= a[i];
    }
    println!("{}", den as f64 / num as f64);
}