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: Wrong Answer)

#include <stdio.h>

#define MAX_SIZE 1000000

int main(void) {
    int s, i=0, prev, flag=0, index, a[MAX_SIZE];
    for (int i = 0; i < MAX_SIZE; i++) {
        a[i] = MAX_SIZE+1;
    }
    if (scanf("%3d", &s) != EOF) {
        prev = s;
        a[i%MAX_SIZE] = s;
        for (i = 1; i < MAX_SIZE; i++) {
            if (prev % 2 == 0) {
                index = (prev/2)%MAX_SIZE;
                if (a[index] == MAX_SIZE+1) {
                    a[index] = prev/2;
                } else {
                    flag = 1;
                }
                prev = prev / 2;
            } else {
                index = (prev*3+1)%MAX_SIZE;
                if (a[index] == MAX_SIZE+1) {
                    a[index] = prev*3+1;
                } else {
                    flag = 1;
                }
                prev = prev*3 + 1;
            }
            if (flag) break;
        }
        printf("%d", i+1);
    }
    return 0;
}