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::Read;

fn main() {
    let (_,a) = {
        let inputstr = {
            let mut inputstr = String::new();
            std::io::stdin().read_to_string(&mut inputstr).unwrap();
            inputstr
        };
        let mut inputiter = inputstr.split_whitespace();
        let n =  inputiter.next().unwrap().parse::<usize>().unwrap();
        let a:Vec<usize> = (1 .. n+1)
            .map(|_|{
                inputiter.next().unwrap().parse::<usize>().unwrap()
            })
            .collect::<Vec<_>>();
        (n,a)
    };
    struct Bunsuu{
        bunshi:usize,
        bunbo:usize
    }
    fn yuclid(a:usize,b:usize)->usize{
        let max = if a > b {a} else {b};
        let min = if a > b {b} else {a};
        let r = max % min;
        if r == 0{
            return min
        }
        return yuclid(min,r)
    }
    impl Bunsuu{
        fn tasizan(&self,x:Bunsuu) -> Bunsuu{
            let bunbo = self.bunbo * x.bunbo;
            let bunshi = self.bunbo*x.bunshi + x.bunbo*self.bunshi;
            let yakusuu = yuclid(bunbo,bunshi);
            Bunsuu{bunshi:bunshi/yakusuu,bunbo:bunbo/yakusuu}
        }
    }
    let ansbunbo = a.into_iter()
        .map(|x|Bunsuu{bunshi:1,bunbo:x})
        .fold(Bunsuu{bunshi:0,bunbo:1},|a,b|a.tasizan(b));
    let ans:f64 = ansbunbo.bunbo as f64/ansbunbo.bunshi as f64;
    println!("{}",ans);
}