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.*;

public class mtwodsix
{

   public static void main(String[] args)
   {
      Scanner sc = new Scanner(System.in);
      int T = sc.nextInt();
      for (int tt = 0; tt < T; tt++)
      {
         int n = sc.nextInt();
         if (n == 1)
         {
            System.out.println(0);
            continue;
         }
         int num_two = num_two(n);
         int num_three = num_three(n);
         if (num_two > num_three || otherfact(num_two, num_three, n))
         {
            System.out.println(-1);
         }
         else if (num_two == num_three)
         {
            System.out.println(num_three);
         }
         else
         {
            int ret = (num_three - num_two) + num_three;
            System.out.println(ret);
         }

      }

   }

   public static int num_two(int n)
   {
      int i = 0;
      while (n % 2 == 0)
      {

         i++;
         n /= 2;

      }
      return i;
   }

   public static int num_three(int n)
   {
      int i = 0;
      while (n % 3 == 0)
      {
         n /= 3;
         i++;
      }
      return i;

   }
   public static boolean otherfact(int n2, int n3, int n) 
   {
      while(n2-->0)
         n/=2;
      while(n3-->0)
         n/=3;
      return n>1;
   }

}
