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)

#include<iostream>
#include<string>
#include<algorithm>
#include<bits/stdc++.h>
 
using namespace std;
 
 int main(void){
     int s,a[1000000]={},count=1;
     cin >> s;
     while(s!=1){
         if(s%2==0){
             s=s/2;
             a[count]=s;
         }else{
             s=s*3+1;
             a[count]=s;
         }
         count+=1;
     }
     for(int i=1; i<count; i++){
         for(int j=i+1; j<count; j++){
             if(a[i]==4){
                 cout << count+1 << endl;
                 return 0;
             }
             if(a[i]==a[j]){
            cout << j << endl;
            return 0;
             }
         }
     }
 }