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(void){
    int s = 0;
    scanf("%ld", &s);
    int a[500000] = {0};
    a[1] = s; int flag = 0; int m = 0;
    for(int i = 1; ; i++){
        if(a[i] % 2 == 0){
            a[i+1] = a[i] / 2;
        }else {
            a[i+1] = 3 * a[i] + 1;
        }
        if(s == 2 || s == 1){
            m = 4;
            flag = 1;
        }else {
            if(i > 1){
                if(a[i-1] == 4 && a[i] == 2 && a[i+1] == 1){
                    m = i + 2;
                    flag = 1;
                }
            }
        }
        if(flag == 1) break;
    }
    printf("%d\n", m);
    return 0;
}