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>
#include<stdlib.h>
#include<string.h>


int f(int n) {
    if(n % 2 == 0) {
        return (int)(n / 2);
    }
    else{
        return 3 * n + 1;
    }
}

int main(void){
    int s;
    scanf("%d", &s);

    int a[1000000] = {0};
    a[1] = s;
    int hist[1000000] = {0};
    hist[a[1]] = 1;

    int i = 2;
    int j;
    while(1){
        a[i] = f(a[i-1]);
        if(hist[a[i]] == 1) {
            printf("%d\n", i);
            return 0;
        }
        else{
            hist[a[i]] = 1;
        }
        i++;
    }
}