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

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import java.util.*;
public class Main
{
	public static void main(String[] args) {
	Scanner sc=new Scanner(System.in);
      int t=sc.nextInt();
     while(t-->0)
     {
        int n=sc.nextInt();
        int s=0,d=0;
        while(n%2==0)
        {
            s++;
            n=n/2;
        }
        while(n%3==0)
        {
          d++;
          n=n/3;
        }
        int ans;
        
        if(n!=1)
        ans=-1;
        else if(d>=s)
        {
            ans=s+(d-s)*2;
            if(s==0&&d==0)
            ans=1;
        }
        else ans=-1;
        System.out.println(ans);
     }
	}
}