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 requiredRemainder{
    //main code
    public static void main (String[] args) throws java.lang.Exception
	{
	    /*Scanner sc = new Scanner(new FileReader("input.txt")); 
		PrintWriter out=new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));*/
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new
         FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 1024);
		//Scanner sc=new Scanner(System.in);
		FastReader sc=new FastReader();
		int t=sc.nextInt();
		while(t-->0){
		    int n=sc.nextInt();
		    int c=0;
		    while(n>=10){
		        if(n==1){
		            break;
		        }
		        c++;
		        if(n%6==0){
		            n/=6;
		        }
		        else n*=2;
		    }
		    //System.out.println(n);
		    if(n==3){
		        c+=2;
		    }
		    else if(n==6){
		        c+=1;
		    }
		    else if(n==9){
		        c+=4;
		    }
		    else if(n!=1){
		        c=-1;
		    }
		    out.write(c+"\n");
		}
		out.flush();
    }
	//fun
	
    //Fast I/O
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
}