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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<iostream>
using namespace std;

int main(){
    int a[1000000];
    int s;
    cin>>s;
    a[0]=s;
    int flag=1;
    for (int i = 1; i < 1000000; i++)
    {
        if (a[i-1]%2==0)
        {
            a[i] = a[i-1]/2;
        }
        else
        {
            a[i] = 3 * a[i-1] +1;
        }

        for (int j = 0; j < i; j++)
        {
            if (a[j]==a[i])
            {
                cout<<i;
                flag=0;
                break;
            }
            
        }
        if (flag==0)
        {
            break;
        }
        
        
        
    }
    
    
}