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: Wrong Answer)

//
//  main.cpp
//  AC
//
//  Created by makinofuya on 2019/07/08.
//  Copyright © 2019 makinofuya. All rights reserved.
//
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <stack>
#include <math.h>
typedef long long ll;
using namespace std;
#define mod 1000000007
#define rep(i,n) for(ll i=0;i<n;i++)
#define out(s) cout << s << endl


int main(){
    int s;cin >> s;
    int i=2;
    int f,tmp=s;
    while(1){
        if(tmp%2==0){
            f=tmp/2;
        }
        else{
            f=3*tmp+1;
        }
        
        if(f==2 && tmp==4){
            cout << i+2 << endl;
            return 0;
        }
        
        tmp=f;
        i++;
    }
}