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: Accepted)

#[allow(unused_macros)]
macro_rules! get {
    ([$t:ty] ; $n:expr) => {
        (0..$n)
        .map(|_| get!([$t])).collect::<Vec<_>>()
    };
    ($($t:ty),+ ; $n:expr) => {
        (0..$n).map(|_| get!($($t),+)).collect::<Vec<_>>()
    };
    ([$t:ty]) => {
        rl().split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect::<Vec<$t>>()
    };
    ($t:ty) => {
        rl().parse::<$t>().unwrap()
    };
    ($($t:ty),*) => {
        {
            let line =rl();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap()),*)
        }
    };
}
fn rl() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}

fn gcd(a: usize, b: usize) -> usize {
    let mut a = a;
    let mut b = b;
    while b != 0 {
        let r = b;
        b = a % b;
        a = r;
    }
    a
}
fn lcm(a: usize, b: usize) -> usize {
    return a / gcd(a, b) * b;
}

fn main() {
    let n = get!(usize);
    let v = get!([usize]);
    if n == 1 {
        println!("{}", v[0]);
        return;
    }
    let mut l = lcm(v[0], v[1]);
    if n == 2 {
        let bunbo: f64 = l as f64 / v[0] as f64 + l as f64 / v[1] as f64;
        let ans = l as f64 / bunbo;
        println!("{}", ans);
        return;
    }
    for i in 2..n {
        l = lcm(l, v[i] as usize);
    }
    // eprintln!("l: {}", l);
    let mut bunbo = 0.0;
    for i in 0..n {
        bunbo += l as f64 / v[i] as f64;
    }
    // eprintln!("bunbo: {}", bunbo);
    let ans = l as f64 / bunbo;
    println!("{}", ans);
}