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 C++14 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <vector>
using namespace std;
int main()
{
	int s;
  	cin >> s;
  	
  	vector<int>	value;
  
  	bool flg = true;
  
  	int num = 1;
  
  	while(flg)
    {
      	num++;	
      
    	if(s%2==0)
        {
			s /= 2;
        }
      	else
      	{
      		s = 3*s + 1;
        }
      
      	for(int i=0;i<value.size();i++)
        {
        	if(value[i] == s)
            {
            	printf("%d",num);	
              
              flg = false;
              break;
            }
        }
      
    }

  	return 0;
}