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.*;
import java.io.*;
public class GFG {
      public static void main (String[] args) {
		Scanner sc=new Scanner(System.in);
		PrintWriter out=new PrintWriter(System.out);
		int t=sc.nextInt();
		while (t-->0)
		{
		    int n=sc.nextInt();
		    int c=0,f=0;
		    while(n>1)
		    {
		        if(n%6!=0&&n%3!=0){f=1;
		        break;}
		        if(n%6==0){
		        n/=6;c++;continue;}
		        if(n%3==0){c+=2;n/=3;continue;}
		    }
		    out.println(f==0?c:-1);
		    out.flush();
		}
      }
}