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 buf = String::new();
    let handle = std::io::stdin();
    let s: usize = {
        handle.read_line(&mut buf).unwrap();
        let tmp = buf.trim().parse().unwrap();
        buf.clear();
        tmp
    };
    let mut a: Vec<usize> = vec![];
    let mut now = s;
    let mut n;
    loop {
        a.push(now);
        let next = {
            if a.last().unwrap() % 2 == 0 {
                a.last().unwrap() / 2
            } else {
                a.last().unwrap() * 3 + 1
            }
        };
        if a.contains(&next) {
            n = a.len() + 1;
            break;
        }
        now = next;
    }
    println!("{}", n);
}