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)

#![allow(unused_variables)]
#![allow(unused_imports)]
#![allow(dead_code)]
use std::io;
use std::str::FromStr;
use std::iter::FromIterator;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::mem::{replace, swap};


// abcde
fn read_string() -> String {
    let mut line = String::new();
    io::stdin().read_line(&mut line).unwrap();
    line
}

// -3.2
fn read_as_primitive<T: FromStr>() -> T {
    let s = read_string();
    s.trim().parse().ok().expect("failed to parse input")
}

// 1 -3 0 999
fn read_as_collection<U: FromStr, T: FromIterator<U>>() -> T {
    let s = read_string();
    s.trim().split_whitespace().map(|s| s.parse().ok().expect("failed to parse")).collect()
}

// #.#.###..
fn read_as_chars<T: FromIterator<char>>() -> T {
    let s = read_string();
    s.trim().chars().collect()
}

// 1 abc
fn read_as_pair<T: FromStr, U: FromStr>() -> (T, U) {
    let s = read_string();
    let elems: Vec<_> = s.trim().split_whitespace().collect();
    (
        elems[0].parse().ok().expect("failed to parse"),
        elems[1].parse().ok().expect("failed to parse"),
    )
}

// 1.5 -2 abc
fn read_as_triple<T: FromStr, U: FromStr, V: FromStr>() -> (T, U, V) {
    let s = read_string();
    let elems: Vec<_> = s.trim().split_whitespace().collect();
    (
        elems[0].parse().ok().expect("failed to parse"),
        elems[1].parse().ok().expect("failed to parse"),
        elems[2].parse().ok().expect("failed to parse"),
    )
}

fn collaz(x: i32) -> i32 {
    let ans = if x % 2 == 0 {x / 2} else {3 * x + 1};
    ans
}

fn main() {
    let s: i32 = read_as_primitive();
    let mut idx: usize = 1;
    let mut x: i32 = s;
    let mut bag: HashSet<i32> = HashSet::new();
    while !bag.contains(&x) {
        bag.insert(x);
        x = collaz(x);
        idx += 1;
    }
    println!("{}", idx)
}