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 (gfortran v4.8.4) (judge verdict: Accepted)

program main
   implicit none
   integer s1
   integer:: s(1000000)
   integer i,j
   read(*,*)s1
   s(1)=s1
   do i=1,1000000
      if(mod(s(i),2)==0)then
         s(i+1)=s(i)/2
      else
         s(i+1)=3*s(i)+1
      endif
      do j=1,i
         if(s(i+1)==s(j))then
            write(*,*)i+1
            goto 100
         endif
      enddo
   enddo
100 continue
end program main