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<string.h>

int main(){
	int s;
	scanf("%d", &s);
	int nl[1000000];
	nl[0]=s;
	int i=0, same=0;
	while(i<1000000){
		if(nl[i]%2 == 0){
			nl[i+1]=nl[i]/2;
			//printf("%d:%d\n",i+1, nl[i+1]);
		}
		else{
			nl[i+1]=3*nl[i]+1;
			//printf("%d:%d\n",i+1, nl[i+1]);
		}
		for(int j=0; j<=i; j++){
			if(nl[i+1]==nl[j]){
				same=i+2;
				break;
			}
		}
		if(same != 0){
			printf("%d", same);
			break;
		}
		i++;
	}
	return 0;
}