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 LuaJIT (2.0.4) (judge verdict: Accepted)

local _i={}
for i=1,1 do
    local a=io.read()
    _i[i]={}
    for s in string.gmatch(a,"%S+")do
        _i[i][#_i[i]+1]=s
    end
end

local s=tonumber(_i[1][1])
if(s==1 or s==2)then
  print(4)
  return
end
local i=1
while true do
  if(s==4)then
  	print(i+3)
  	return
  elseif(s%2==0)then
  	s=s*.5
  else
  	s=3*s+1
  end
  i=i+1
end