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.Scanner;

public class Demo {
	
	
	
	public static void main(String [] args)
	{
		Scanner in = new Scanner(System.in);
		
		int t= in.nextInt();
		
		for(int i =0;i<t;i++)
		{
			int n =in.nextInt();

			if(n==1)
			{
				System.out.println("0");
				continue;
			}
			
			int ans =0;
			
			while(n%3==0)
			{
				ans++;
				n =n/3;
			}
			
			if((int)(Math.log(n)/Math.log(2))== Math.log(n)/Math.log(2))
			{
				
					int twos =(int)(Math.log(n)/Math.log(2));
					
					if(ans>=twos)
					{
						System.out.println((ans-twos)+ans);
					}
					else {
						System.out.println("-1");
					}
					
				
				
			}
			else {
				System.out.println("-1");
			}
		}
		
	}

}
