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.util.Scanner;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Iterator;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.math.BigInteger;
public class B1317 
{
	static Scanner sc = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);

	static void pn(Object o) {
		out.println(o);
		out.flush();

	}

	static void p(Object o) {
		out.print(o);
		out.flush();
	}

	static void pni(Object o) {
		out.println(o);
		System.out.flush();
	}

	static int I() throws IOException {
		return sc.nextInt();
	}

	static long L() throws IOException {
		return sc.nextLong();
	}

	static double D() throws IOException {
		return sc.nextDouble();
	}

	static String S() throws IOException {
		return sc.nextLine();
	}

	static char C() throws IOException {
		return sc.next().charAt(0);
	}
	static int[] Ai(int n) throws IOException {
		int[] arr = new int[n];
		
		for (int i = 0; i < n; i++)
			arr[i] = I();
		
		return arr;
	}
	
	static String[] As(int n) throws IOException {
		String s[] = new String[n];
		
		for (int i = 0; i < n; i++)
			s[i] = S();
		
		return s;
	}
	
	static long[] Al(int n) throws IOException {
		long[] arr = new long[n];
		
		for (int i = 0; i < n; i++)
			arr[i] = L();
		
		return arr;
	}
	public static void process() throws IOException
	{
		long n=L();
		int c=0;boolean flag=true;
		while(n!=1)
		{
			
			if(n%6==0)
			{
				n=n/6;c++;
			}
			else
		    if(n%3==0)
		    {
		    	n=n*2;c++;
		    }
		    else
		    {
		    	flag=false;
		    	break;
		    }
		    		  
		}
		if(flag==false)
		{
			pn(-1);
		}
		else
		{
			pn(c);
		}
	}
	public static void main(String[] args) throws IOException {

		int t = I();
		while (t-- > 0)
			process();

	}
}
	