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::stdin;

fn main() {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    let num: i32 = buf.trim().parse().unwrap();

    println!("{}", solve(num));
}

fn solve(num: i32) -> i32{
    let mut array = vec![num];
    let mut counter = 1;
    let mut current = num;
    let mut is_ever ;
    loop {
        counter += 1;
        is_ever = current % 2 == 0;
        match is_ever{
            false => current = 3 * current + 1,
            true => current = current / 2,
        }
        if array.contains(&current){
            return counter
        }

        array.push(current);
    }
}