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 OCaml (4.02.3) (judge verdict: Accepted)

let kMax = 1000000

let _ =
  let s = Scanf.scanf "%d" @@ (+) 0 in
  let flags = Array.make (kMax + 10) false in
  flags.(s) <- true;
  let n = ref s in
  for i = 2 to kMax do
    n := if !n mod 2 = 0 then !n / 2 else 3 * !n + 1;
    if flags.(!n) then (Printf.printf "%d\n" i; exit 0);
    flags.(!n) <- true
  done