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>
#include<cctype>
using namespace std;
#define rep(i,n) for (int i=0;i<(n);i++)
#define all(v) (v).begin(),(v).end()
typedef long long int ll;
#define pi 3.1415926535897932384
#define E9 1000000000
#define eps 1e-4
#define pii pair<int,int>


int main(){
  int s; cin >> s;
  set<int> S;
  int idx = 1;
  while (true){
    if (S.count(s)) break;
    else S.insert(s);

    if (s%2) (s *= 3) += 1;
    else s /= 2;
    
    idx++;
  }

  cout << idx << endl;
  
  // cout << fixed << setprecision(10);
  
  return 0;
}