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 (1.42.0) (judge verdict: Accepted)

use proconio::{input, fastout};

macro_rules! debug {
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
  }

#[fastout]
fn main() {
    input!{
        s: usize,
    }

    let mut cnt = 0;
    let mut a: Vec<usize> = Vec::new();
    a.push(s);
    loop {
        if a[a.len()-1]%2==0 {
            a.push(a[a.len()-1]/2);
        } else {
            a.push(a[a.len()-1]*3+1);
        }
        for i in 0..a.len()-1 {
            if a[a.len()-1]==a[i] {
                println!("{}", a.len());
                return;
            }
        }
    }

}