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

import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
 
public class Solution {
    public static void main(String[] args)throws IOException {
        
    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer tk;    
    
   int t=Integer.parseInt(br.readLine());
   
   for(int test=0;test<t;test++)
   {
        tk=new StringTokenizer(br.readLine());
        int n=Integer.parseInt(tk.nextToken());
        
        int count3=0;
        while(n>0 && n%3==0)
        {
            count3++;
            n=n/3;
            
        }
        
        int count2=0;
        while(n>0 && n%2==0)
        {
            count2++;
            n=n/2;
        }
        
        if(n>1)
        {
            System.out.println("-1");
        }
       else
        {
            
            if(count3<count2)
            {
                System.out.println("-1");
            }
            else
            {
                int ans= (count3-count2) +count3;
                System.out.println(ans);
            }
            
        }
       
   }
  
  
      
    
 }
 
}
 