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)

#include<stdio.h>

int main(){
  int s;
  
  scanf("%d",&s);
  int a[1000000];
  int ans;
  int flag = 0; 
  
  int n = 1;
  a[0] = s;
  while(1){
    if(a[n] / 2 == 0){
      a[n] = a[n - 1] / 2;
    } else {
      a[n] = 3 * a[n - 1] + 1;
    }
    
    int i;
    for(i = 0; i <= n; i++){
      if(a[n] == a[i]){
        ans = n;
        flag = 1;
      }
    }
    if(flag == 1){
      break;
    }
    n += 1;
  }
  printf("%d", ans + 1);
}