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)

/**
 * @copyright (c) 2020 Daisuke Hashimoto
 */

#include <bits/stdc++.h>
using namespace std;
using ll = int64_t;
using Pair = pair<int32_t, int32_t>;

// std::cout << std::setprecision(20) << 1.1 << endl;

int32_t f(const int32_t n) {
  return (n % 2 == 0) ? n / 2 : 3 * n + 1;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  int32_t s;
  cin >> s;
  int32_t value = s;
  int32_t m = -1;
  vector<bool> lookup(1000000 + 1, false);
  lookup[value] = true;
  for (int32_t i = 2; i < 1000002; ++i) {
    value = f(value);
    if (lookup[value]) {
      m = i;
      break;
    } else {
      lookup[value] = true;
    }
  }
  cout << m << endl;

  return 0;
}