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 <bits/stdc++.h>
using namespace std;
 
int main() {
  int s;
  cin>>s;  int X;
  vector<int> A;
  X=s;
  A.push_back(s);
  for(int i=0;i<100000000;i++){
    
    if(X%2==0){
      X=X/2;
      A.push_back(X);
      
      for(int j=0;j<X;j++){
        if(A.at(j)==A.at(i)){
          cout<<i+1<<endl;
          return 0;
        }
      }
    }

      
    if(X%2==1){
      X=X*3+1;
      A.push_back(X);
      
      for(int j=0;j<X;j++){
        if(A.at(j)==A.at(i)){
          cout<<i+1<<endl;
          return 0;
        }
       }
    }
  }
}