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::collections::HashSet;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();

    let s = buf.trim().parse::<i32>().unwrap();

    let mut results = HashSet::new();

    results.insert(s);
    let mut v = s;
    for (index, _) in (s-1000000..s).rev().enumerate() {
        let index = index + 2;
        v = func(v);
        if results.contains(&v) {
            println!("{}", index);
            break;
        }
        results.insert(v);
    }
}
fn func(n: i32) -> i32 {
    return if n % 2 == 0 {
        n / 2
    } else {
        3 * n + 1
    }
}