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 <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <map>

#define rep(i,n) for (int i = 0; i < n; ++i)
#define repr(i,n) for (int i = n; i > 0; --i)
using namespace std;
using ll = long long;
using P = pair<int,int>;

const int MAX = 100;
const int INF = (1<<12);

int main() {
  int s;
  cin >> s;
  map<int,int> A;
  int i = 1;
  A[s] = i;
  while(1){
    if(s%2 == 0) {
      s /= 2;
    }
    else {
      s = 3 * s + 1;
    }
    i++;
    if(A[s]) {
      break;
    }
    else {
      A[s] = i;
    }
  }
  cout << i << endl;
  return 0;
}