Problem:
Score : 100 points

Problem Statement

Given is an integer N.

Takahashi chooses an integer a from the positive integers not greater than N with equal probability.

Find the probability that a is odd.

Constraints

1 \leq N \leq 100

Input

Input is given from Standard Input in the following format:

N

Output

Print the probability that a is odd.
Your output will be considered correct when its absolute or relative error from the judge's output is at most 10^{-6}.

Sample Input 1

4

Sample Output 1

0.5000000000

There are four positive integers not greater than 4: 1, 2, 3, and 4. Among them, we have two odd numbers: 1 and 3. Thus, the answer is \frac{2}{4} = 0.5.

Sample Input 2

5

Sample Output 2

0.6000000000

Sample Input 3

1

Sample Output 3

1.0000000000

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn vs(a: &mut Vec<Vec<usize>>, n: usize, p1: usize, p2: usize, done: &mut Vec<bool>) -> bool {
    if done[p2 - 1] {
        a[p1 - 1].push(p2);
        done[p1 - 1] = true;
        return false;
    } else if let Some(p3) = a[p2 - 1].pop() {
        if p1 != p3 {
            done[p1 - 1] = true;
            a[p1 - 1].push(p2);
            return vs(a, n, p2, p3, done);
        }
        done[p1 - 1] = true;
        done[p2 - 1] = true;
        return true;
    }
    false
}

fn day(a: &mut Vec<Vec<usize>>, n: usize) -> u32 {
    let mut done: Vec<bool> = vec![false; n];
    let mut cnt: u32 = 0;
    for p1 in 1..(n + 1) {
        if done[p1 - 1] {
            continue;
        } else if let Some(p2) = a[p1 - 1].pop() {
            if vs(a, n, p1, p2, &mut done) {
                cnt += 1;
            }
        }
    }
    cnt
}

fn all(a: &mut Vec<Vec<usize>>, n: usize) -> i32 {
    let mut vs_cnt: u32 = 0;
    let mut day_cnt: i32 = 0;

    while vs_cnt < ((n * (n - 1)) / 2) as u32 {
        let tmp = day(a, n);
        if tmp == 0 {
            day_cnt = -1;
            break;
        } else {
            vs_cnt += tmp;
        }
        day_cnt += 1;
    }

    return day_cnt;
}

fn main() {
    let n: u32 = read();
    println!("{}", (((n + 1) / 2) as f32) / (n as f32));
}