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.lang.*;
import java.io.*;

public class Codechef
{
    final static  long mod=0x3f3f3f3f3f3f3f3fL; 
    final static long modules=10000007;
    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; 
        } 
        
        int mygcd(int a, int b)
        {
	if(b == 0){
		return a;
	}
	return mygcd(b, a % b);
        }
        
        int mypow(int a, int b) {
	int res = 1;
	while(b>0) {
		if((b & 1)>0)
			res = (int)((res * a) % mod);
		a = (int)(( a*a)%mod);
		b >>= 1;
	}
	return res;
        }
    } 
      
    public static void main (String[] args) throws java.lang.Exception
    {
        FastReader sc=new FastReader();
        int t=sc.nextInt();
        while(t-- >0)
        {
            int m=sc.nextInt();
            int w=0,flag=0;
            while(m!=1)
            {
                if(m>1)
                {
                    if(m%6==0)
                    {
                        m/=6;
                        w++;
                    }
                    else
                    {
                        m*=2;
                        if(m%2==0 && m%3!=0)
                        {
                            flag=1;
                            break;
                        }
                        w++;
                    }
                }
                else
                {
                    m*=2;
                    w++;
                }
            }
            if(flag==1)
                System.out.println("-1");
            else
                System.out.println(w);
        }
    }      
}
