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 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll a[100000500];
ll memory[100000500];
ll u=1;
ll stroage(ll n)
{
    for(int i=1; i<=u; i++)
        if(memory[i]==n)
            return 1;
    memory[u++]=n;
    return 0;
}
int main()
{
    ll s;
    cin>>s;
    a[1]=s;
    stroage(s);
    for(ll i=2;;i++)
    {

        if(a[i-1]%2==0)
        {
            a[i]=a[i-1]/2;
            if(stroage(a[i])==1)
            {
                cout<<i<<endl;
                break;
            }
        }
        else if(a[i-1]%2==1)
        {
            a[i]=3*a[i-1]+1;
        if(stroage(a[i])==1)
            {
                cout<<i<<endl;
                break;
            }

        }
    }
    return 0;
}