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>

unsigned short a[1000000];

int main(void)
{
	unsigned short s;
	int i,j;
	scanf("%hu",&s);
	a[0] = s;

	for (i=1;i<1000000;i++) {
		if (a[i-1]%2==0) {
			a[i] = a[i-1] / 2;
		} else {
			a[i] = 3*a[i-1] + 1;
		}
		// printf("%hd\n",a[i]);

		for (j=0;j<i;j++) {
			if (a[i] == a[j]) {
				printf("%d\n",i+1);
				return 0;
			}
		}
	}
	
	return 0;
}