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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 * 
 */

/**
 * @author rajee
 *
 */
public class CodeForces1374B {

    /**
    * 
    * Function name - main
    * Description   - 
    * @param     - 
    * @return        - void
    */
    public static void main(String[] args) { 
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
       
        final int cases;
        try {
            cases = Integer.parseInt(br.readLine().trim());      
            
            for (int t = 1; t <= cases; t++) {
                
                int n = Integer.parseInt(br.readLine().trim());
                int steps = 0;
                while(n!=1) {
                    if(n%6 == 0) {
                        n = n/6;
                        steps++;
                    }else if( (n*2) % 6 == 0) {
                        n = n *2;
                        steps++;
                    }else {
                        steps = -1;
                        break;
                    }
                }
                System.out.println(steps);
            }
            
           
           

        } catch (IOException e) {
            
            e.printStackTrace();
        }
       
       
    }

}
