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;
         }
         HashMap<Integer, Integer> primefactorization = pfac(n);
         boolean flag = false;
         for (Integer i : primefactorization.keySet())
         {
            if (i == 3)
            {
               flag = true;
            }
         }
         if (!flag)
         {
            System.out.println(-1);
            continue;
         }
         int num_two = 0;
         if (primefactorization.keySet().contains(2))
            num_two = primefactorization.get(2);
         int num_three = primefactorization.get(3);
         if (num_two > num_three)
         {
            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 HashMap<Integer, Integer> pfac(int n)
   {
      int i = 2;
      HashMap<Integer, Integer> ret = new HashMap<Integer, Integer>();
      while (n > 1 && i <= n)
      {
         if (n % i == 0)
         {
            if (!ret.keySet().contains(i))
            {
               ret.put(i, 0);
            }
            int val = ret.get(i) + 1;
            ret.put(i, val);
            n /= i;
         }
         else
         {
            i++;
         }
      }
      return ret;
   }

}
