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.util.ArrayList;
import java.util.Scanner;

/**
 *
 * @author slmns
 */
public class MultiplyBy2DivideBy6 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int t = Integer.parseInt(scan.nextLine());
        int counter = 0;
        ArrayList list = new ArrayList();
        
        for (int i = 0; i < t; i++) {
            int n = Integer.parseInt(scan.nextLine());
            
           
            if (n != 1){
                counter++;
                while(n!=1 && counter >= 1){
                    if(n%6==0){
                        n/=6;
                        counter++;
                    }else{
                        n*=2;
                        counter++;
                    } if(counter==100){
                        counter*=0;
                        list.add("-1");
                        
                    }
                    
                }
                    
            }
             if(n == 1 && counter==0){
                list.add(counter);
                
             }else if(n==1 && counter>0){
                 counter-=1;
                list.add(counter);
                 counter*=0;
             }
                    
            
        }
        for (int i = 0; i < t; i++) {
            System.out.println(list.get(i));
        }
        
    }
    
}
