Score : $200$ points
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:
Input is given from Standard Input in the following format:
$s$
Print the minimum integer $m$ that satisfies the condition.
8
5
$a=\{8,4,2,1,4,2,1,4,2,1,......\}$. As $a_5=a_2$, the answer is $5$.
7
18
$a=\{7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1,......\}$.
54
114