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>
#define MAX_M 100000
int f(int);
int main(){
    int s,m,flag=0;
    int a[MAX_M];
    scanf("%d",&s);
    a[1] = s;

    for(int i=1;i<MAX_M;i++){
        a[i+1]=f(a[i]);
        for(int j=1;j<i;j++){
            if(a[i]==a[j]){
                m=i;
                flag=1;
                break;
            }
        }
        if(flag==1) break;
    }

    printf("%d",m);

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