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 read_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim_right().to_owned()
}

fn str_to_ints(s: String) -> std::vec::Vec<i64> {
    let mut ret = std::vec::Vec::new();
    let ws = s.split_whitespace();
    for w in ws {
        ret.push(w.parse().unwrap());
    }
    ret
}

fn read_ints() -> std::vec::Vec<i64> {
    str_to_ints(read_line())
}

fn f(n: i64) -> i64 {
    if n % 2 == 0 {
        n / 2
    } else {
        3 * n + 1
    }
}

fn main() {
    let s = read_ints()[0];
    let mut set_a: std::collections::HashSet<i64> = std::collections::HashSet::new();

    let mut a: i64 = s;
    for i in 0..1000000 {
        if set_a.contains(&a) {
            println!("{}", i + 1);
            break;
        }
        set_a.insert(a);
        a = f(a);
    }
}