Collatz conjecture, also known as 3n+1 problem, which is a conjecture in mathematics that is about a sequence defined as follows:
Let $S_1$ be a positive integer which is the start of the sequence, and

$
S_{n+1}=
\begin{align}
\begin{cases}
S_n\ /\ 2&,\text{if }S_n\text{ is even} \\
3\ S_n\ +\ 1&,\text{if }S_n\text{ is odd} \\
\end{cases}
\end{align}
$

The conjecture is that for any given positive integer $S_1\ (<10^ 5)$, the sequence will reach $1$.
e.g. Given $S_1 = 22$,
the sequence will be: $22\ 11\ 34\ 17\ 52\ 26\ 13\ 40\ 20\ 10\ 5\ 16\ 8\ 4\ 2\ 1$

As students of NCKU, we are interested in this conjecture,
please write a program to help us do some research in this conjecture.