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<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<map>
#include<cmath>
#include<string>
#include<bitset>
#include <sstream>
#include<queue>
#include<set>
#define rep(i,n) for(ll i=0;i<(n);++i)
using namespace std;
typedef long long ll;
typedef pair<int,ll>P;

int main()
{
    int s;
    cin>>s;
    ll prev=s;
    map<ll,int> a;
    ll ans=1;
    ll towans=0;
    a[s]++;
    while(1)
    {
        ans++;
        ll tempa=0;
        if(prev%2==0)
        {
            tempa=prev/2;
        }
        else
        {
            tempa=3*prev+1;
        }
        if(a[tempa]==0)
        {
            a[tempa]++;
        }
        else
        {
            break;
        }
        prev=tempa;
        
    }
    cout<<ans<<endl;
}