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::Read;

fn main() {
    let mut buf = String::new();

    std::io::stdin().read_to_string(&mut buf).unwrap();

    let mut iter = buf.split_whitespace();
    let s: usize = iter.next().unwrap().parse().unwrap();

    let mut a: Vec<usize> = vec![s];

    let mut prev = s;

    if s == 1 || s == 2 || s == 4 {
        println!("{}", 4);
    } else {
        loop {
            let next = if prev % 2 == 0 {
                prev / 2
            } else {
                3 * prev + 1
            };
            a.push(next);

            if next == 4 {
                break;
            }
            prev = next;
        }

        // for item in &a{
        //     print!("{} ", item);
        // }

        println!("{}", a.len() + 3);
    }

    // println!("{}", ab * bc / 2);
}