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>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define repr(i, n) for (int i = (n); i >= 0; --i)
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define FORR(i, m, n) for (int i = (m); i >= (n); --i)
using namespace std;
typedef long long ll;
const ll mod = 1000000007;
const ll mod2 = 998244353;

int main() {
  vector<int> a(1000005);
  vector<bool> e(1000005);
  cin >> a[0];
  e[a[0]] = true;
  rep(i, 1000005) {
    if (a[i] % 2 == 0) {
      a[i+1] = a[i] / 2;
    }
    if (a[i] % 2 == 1) {
      a[i+1] = 3 * a[i] + 1;
    }
    if (e[a[i+1]]) {
      cout << i+2 << endl;
      break;
    }
    if (!e[a[i+1]]) {
      e[a[i+1]] = true;
    }
  }
}