Problem:
Score : 200 points

Problem Statement

A sequence a=\{a_1,a_2,a_3,......\} is determined as follows:

The first term s is given as input.

Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.

a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.

Find the minimum integer m that satisfies the following condition:

There exists an integer n such that a_m = a_n (m > n).

Constraints

1 \leq s \leq 100

All values in input are integers.

It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.

Input

Input is given from Standard Input in the following format:

s

Output

Print the minimum integer m that satisfies the condition.

Sample Input 1

8

Sample Output 1

5

a=\{8,4,2,1,4,2,1,4,2,1,......\}. As a_5=a_2, the answer is 5.

Sample Input 2

7

Sample Output 2

18

a=\{7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1,......\}.

Sample Input 3

54

Sample Output 3

114

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

fn main() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let s: u32 = s.trim_right().to_owned().parse().unwrap();

    let mut an: Vec<u32> = Vec::new();
    an.push(s);
    loop {
        let m = an.len();
        let am = {
            if &an[m - 1] % 2 == 0 {
                an[m - 1] / 2
            } else {
                3 * an[m - 1] + 1
            }
        };
        an.push(am);
        for n in 0..(an.len()-1) {
            if an[n] == am {
                println!("{}", m + 1);
                std::process::exit(0);
            } 
        };
    };

}