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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;
import javafx.scene.shape.TriangleMesh;

/**
 *
 * @author USER
 */
public class Cf {
    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; 
        } 
    } 
    
    static class BufPrint
    {
        final BufferedWriter bw;
        public BufPrint()
        {
            this.bw=new BufferedWriter(new OutputStreamWriter(System.out));
        }
        public void print(Object object)throws IOException
        {
            bw.append(""+object);
        }
        public void println(Object object)throws IOException
        {
            print(object);
            bw.append("\n");
        }
        public void close()throws IOException
        {
            bw.close();
        }
    }
    

        public static int GCD(int l,int r) {
        int gcd=1;
        for(int i = 1; i <= l && i <= r; ++i)
        {
            // Checks if i is factor of both integers
            if(l % i==0 && r % i==0)
                gcd = i;
        }
    return gcd;
}
    
    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException{
        // TODO code application logic here
        
            FastReader sc=new FastReader(); 
            BufPrint bp=new BufPrint();
          

                
                               
                
               int t=sc.nextInt();
                    
               for(int k1=0;k1<t;k1++)
               {
                   long n=sc.nextLong();
                   
                   int c=0;
                  boolean flag=true;
                   if(n%3==0){
                   while(n!=1)
                   {
                      if(n%6==0)
                      {
                          n=n/6;
                          c++;
                      }
                      else if(n%3==0)
                      {
                          n=n*2;
                          c++;
                      }
                      else
                      {
                          flag=false;
                          break;
                      }
                   }
                   }
                   else if(n==1)
                   {
                       flag=true;
                   }
                   else
                   {
                       flag=false;
                   }
                   
                   if(flag==true)
                   {
                       bp.println(c);
                   }
                   else
                   {
                       bp.println(-1);
                   }
                
                        

                
                
		
                   



                   
                   
               
                
               
 
 
 
               }         

                
           
                bp.close();
            
    }
}