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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
// B
fscanf(STDIN, '%d', $s);
$n = 1000000;
$ap = $s;
$c = array_fill(0, $n, false);
$c[$s] = true;
for ($i = 2; $i <= $n; $i++) {
    $a = f($ap);
    if ($c[$a]) break;
    $c[$a] = true;
    $ap = $a;
}
echo $i;

function f($n)
{
    return ($n & 1) ? 3 * $n + 1 : $n / 2;
}