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>

int main(){
    int s;
    int i, j, a[10000], min = 10000, ansj;

    scanf("%d", &s);

    a[0] = s;

    for(i=1; i<10000; i++){
        if(a[i-1] % 2 == 0)
            a[i] = a[i-1] / 2;
        else
            a[i] = 3 * a[i-1] + 1;
    }

    for(i=0; i<10000; i++){
        for(j=0; j<10000; j++){
            if(j > i && a[i] == a[j]){
                if((j-i) < min){
                    min = j - i;
                    ansj = j;
                }
            }
        }
    }

    printf("%d\n", ansj + 1);

    return 0;
}