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.Scanner;

public class MultiplyBy2DivideBy6 {

    public static int[] hasOtherDivisor(int n){

        int ans[]=new int[2];
        
        while (n%3==0){
                n/=3;
                ans[1]++;
        
        }
        
        
        if( Math.pow(2, (int)(Math.log(n) / Math.log(2)))==n)
            ans[0]=(int)(Math.log(n) / Math.log(2));
        else{
            ans[1]=-1;
            ans[0]=-1;
        }
    return ans;
    }

    public static void main(String[] args) {

        Scanner s = new Scanner(System.in);

        int t = s.nextInt();
        for(int i=0;i<t;i++) {

            int n=s.nextInt();

            if(n==1)
                System.out.println(0);
            else if(n==3)
                System.out.println(2);
            else if(n%3!=0)
                System.out.println(-1);

        else{
                int ans2[]=new int[2];
                ans2=hasOtherDivisor(n);
                
                int num2=ans2[0], num3=ans2[1];
                
                if(num2==-1 && num3==-1)
                    System.out.println(-1);
                else if(num2>num3){
                    System.out.println(-1);
                }
                else if(num2==num3)
                    System.out.println(num2);
                else if(num2<num3)
                    System.out.println(num3-num2+num3);
            }
        }
    }
}
