You are given an integer n. In one move, you can either multiply n by two or divide n by 6 (if it is divisible by 6 without the remainder).

Your task is to find the minimum number of moves needed to obtain 1 from n or determine if it's impossible to do that.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow. 

The only line of the test case contains one integer n (1 ≤ n ≤ 10^9).

Output

For each test case, print the answer — the minimum number of moves needed to obtain 1 from n if it's possible to do that or -1 if it's impossible to obtain 1 from n.

Example

Input


7
1
2
3
12
12345
15116544
387420489


Output


0
-1
2
-1
-1
12
36

Note

Consider the sixth test case of the example. The answer can be obtained by the following sequence of moves from the given integer 15116544:

  1. Divide by 6 and get 2519424; 
  2. divide by 6 and get 419904; 
  3. divide by 6 and get 69984; 
  4. divide by 6 and get 11664; 
  5. multiply by 2 and get 23328; 
  6. divide by 6 and get 3888; 
  7. divide by 6 and get 648; 
  8. divide by 6 and get 108; 
  9. multiply by 2 and get 216; 
  10. divide by 6 and get 36; 
  11. divide by 6 and get 6; 
  12. divide by 6 and get 1. 
1
999838675

-1

/******************************************************************************

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import java.util.*;
public class Main
{
	public static void main(String[] args) {
	Scanner sc=new Scanner(System.in);
      int t=sc.nextInt();
      boolean f[]=new boolean [100001];
       ArrayList<Integer> a=new ArrayList<>();
       
       for(int i=2;i*i<100001;i++)
       {
             if(!f[i])
             {
                   for(int j=i*i;j<100001;j+=i)
                    f[j]=true;
             }
       }
       for(int i=2;i<100001;i++)
       if(!f[i])
       a.add(i);
       
      while(t-->0)
      {
        int n=sc.nextInt();
         int c=0;
       for(int i=2; i<a.size();i++)
        {
           if(n%a.get(i)==0)
           {
                 c++;
                 break;
           }
           
     }
     if(n==1)
     System.out.println("0");
   else if(c>=1)
   System.out.println("-1");
   else 
   {
         int s,d;
         s=d=0;
         int i=2;
         while(i<=n && n%i==0)
            {s++;i=i*2;
            }
            i=3;
             while(i<=n && n%i==0)
            {d++;i=i*3;
            }
            if(s>d || d==0)
            {
                  System.out.println("-1");
            }
            else
            {
                  if(s==d)
                  {
                        System.out.println(n/6); 
                  }
                  else
                  {
                      n=n*(int)Math.pow(2,d-s);
                      
                    
                         System.out.println(d+(d-s)); 
                  }
            }
   }
  
      
      
      }      
     }
}