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 (GCC 5.4.1) (judge verdict: Wrong Answer)

// Ver19.02
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#define INF 1 << 29
#define LLINF 4545454545454545454
#define MOD 1000000007
#define ll long long
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define MIN(a, b) ((a) < (b) ? (a) : (b))
int upll(const void *a, const void *b) { return *(ll *)a < *(ll *)b ? -1 : *(ll *)a > *(ll *)b ? 1 : 0; }
int downll(const void *a, const void *b) { return *(ll *)a < *(ll *)b ? 1 : *(ll *)a > *(ll *)b ? -1 : 0; }
void sortup(ll *a, int n) { qsort(a, n, sizeof(ll), upll); }
void sortdown(ll *a, int n) { qsort(a, n, sizeof(ll), downll); }

ll collatz(ll x)
{
  if (x % 2 == 0)
  {
    return x / 2;
  }
  else
  {
    return 3 * x + 1;
  }
}

int main()
{
  ll s;
  ll a[1000001];
  scanf("%lld", &s);
  for (int i = 0;; i++)
  {
    ll maybe = collatz(s);
    for (int j = 0; j < i; j++)
    {
      if (a[j] == maybe)
      {
        printf("%d\n", i + 2);
        return 0;
      }
    }
    a[i] = maybe;
    s = maybe;
  }
}