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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Submit {
    static int ans=0;
    public static void main(String args[]) throws IOException{
        process();
    }
    public static void process() throws IOException{
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        int T=Integer.parseInt(in.readLine());
        for(int t=0;t<T;t++){
            ans=0;
            int n=Integer.parseInt(in.readLine());
            boolean flag=true;
            while(true){
                n=six(n);
                if(n==1)
                    break;
                if(n%3!=0){
                    flag=false;
                    break;
                }
                n*=2;
                ans++;
                n=six(n);
            }
            if(flag)
                System.out.println(ans);
            else
                System.out.println("-1");
        }
    }
    public static int six(int n){
        while(n%6==0 && n>1) {
            n /= 6;
            ans++;
        }
        return n;
    }
}
