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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

#define TRUE (1)
#define FALSE (0)

int is_in_numlist (
    int *numlist,
    int list_elem_num,
    int target)
{
    int i;
    for (i = 1; i < list_elem_num; i++) {
        if ( numlist[i] == target ) {
            return TRUE;
        }
    }
    return FALSE;
}

int main (void) {
    int s;
    scanf("%d", &s);

    int numlist[1000001];
    numlist[1] = s;
    int i = 1;

    do {
        i++;
        if ( s % 2 == 0 ) {
            s /= 2;
        }
        else {
            s = 3 * s + 1;
        }
        numlist[i] = s;
    }  while ( is_in_numlist(numlist, i, s) == FALSE );

    printf("%d\n", i);
    return 0;
}