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 Julia (0.5.0) (judge verdict: Accepted)

const lines=readlines()
state=0
input()=lines[global state+=1]
int(s::String)=parse(Int32,s)
intSub(s::SubString{String})=parse(Int32,s)
floatSub(s::SubString{String})=parse(Float64,s)
intLine()=map(intSub,split(input()))
function f(n::Int32)::Int32
    if n%2<1
        return div(n,2)
    else
        return 3n+1
    end
end
function main()
    s=int(input())
    a=zeros(Bool,10^7)
    a[s]=true
    n=1
    while true
        s=f(s)
        n+=1
        if a[s]
            println(n)
            break
        else
            a[s]=true
        end
    end
end
main()