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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
$N = (int)(trim(fgets(STDIN)));
$new_arr = [];
$count = 2;
function fun($number){
    if($number%2 === 0){
        return $number/2;
    }else{
        return 3*$number+1;
    }
}

while (true){
    $new_n = fun($N);
    if(in_array($new_n,$new_arr,true)){
        break;
    }
    array_push($new_arr,$new_n);
    $count += 1;
    $N = $new_n;
}
echo $count;