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 s = String::new();
    stdin().read_line(&mut s).ok();
    let vs: Vec<u32> = s.trim().split_whitespace().map(|token| token.parse().ok().unwrap()).collect();
    let mut a = vec![0, vs[0]];
    let mut lasta = vs[0];
    for i in 2..1_000_000 {
        let an = if lasta % 2 == 0 {
            lasta / 2
        } else {
            3 * lasta + 1
        };
        if a.iter().any(|ak| *ak == an) {
            print!("{}", i);
            return;
        } else {
            a.push(an);
            lasta = an;
        }
    }
}