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>
#include<string.h>
#include<stdlib.h>
#include<math.h>
#define max(x,y)(x>y?x:y)
#define min(x,y)(x>y?y:x)
typedef long long int ll;
typedef unsigned long long int ull;
int asc_cmp(const void* X,const void* Y){int x=*(int*)X,y=*(int*)Y;if(x<y)return -1;else if(x==y)return 0;else return 1;}
int desc_cmp(const void* X,const void* Y){int x=*(int*)X,y=*(int*)Y;if(x<y)return 1;else if(x==y)return 0;else return -1;}

int main(){
    int s;scanf("%d",&s);
    int x=s;
    int flg[2000000]={};
    flg[s]=1;
    int cnt=1;
    while(1){
        if(x%2)x=3*x+1;
        else x=x/2;
        cnt++;
        if(flg[x])break;
        flg[x]=1;
    }
    printf("%d\n",cnt);
}