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: Accepted)

#include <stdio.h>
 
int main() {
   int s, i = 0, j = 0, cnt = 0;
   int a[1000000];
   
   scanf("%d",&s);
   a[i] = s;

   if((s < 1) || (s > 100)) {
      return 0;
   }
   
   while (i < 1000000) {
     j = 0;
     cnt = 0;
     while (j <= i) {
        if (a[i] == a[j] ) {
           cnt++;
           if(cnt == 2) {
              printf("%d\n",j + 1);
              return 0;
           }
        }
        j++;
     }
     if (a[i] % 2 == 0)  {
        a[i + 1] = a[i] / 2;
     }
     else if (a[i] % 2 != 0)  {
        a[i + 1] = 3 * a[i] + 1;
     }
     
     i++;
   }
}