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 Fortran (GNU Fortran 9.2.1) (judge verdict: Accepted)

program sample
    implicit none
  
    integer(8) :: i,j,m,n,x,b,s
    
    integer(8):: a(1000000)
  
    read(*,*) s
    
    
    do i=1,1000000
        a(i)=0
    end do
    m=1
    do 
        if(a(s)==1)then
            exit
        else
            a(s)=a(s)+1
            m=m+1
            if (mod(s,2)==0)then
                s=s/2
            else
                s=s*3+1
            end if
        end if
                 
    end do
   
        write(*,*)m
   
    
    stop
end program sample