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::marker::Chars;
use proconio::{fastout, input};
// use std::cmp::{max, min};

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

    let mut count = 1;
    let mut n = s;
    let mut v = vec![n];
    loop {
        count += 1;
        n = if n % 2 == 0 { n / 2 } else { 3 * n + 1 };
        // println!("{}", n);
        if v.contains(&n) {
            break;
        } else {
            v.push(n);
        }
    }

    println!("{}", count);
}