B - Collatz 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.

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