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)

use std::io;

fn main() {
    let mut s = String::new();
    let _ = io::stdin().read_line(&mut s);

    let num = s.trim_right().parse::<usize>().unwrap();

    let mut v = vec![num];
    let mut i = 0;
    loop {
        let num = v[i];

        let x = if is_even(num) {
            even_func(num)
        } else {
            odd_func(num)
        };
        if v.contains(&x) {
            println!("{}", i + 2);
            break;
        }

        v.push(x);
        i += 1;
    }

}

fn is_even(num: usize) -> bool {
    num % 2 == 0
}

fn even_func(num: usize) -> usize {
    num / 2
}

fn odd_func(num: usize) -> usize {
    3 * num + 1
}