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 Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		try (Scanner reader = new Scanner(System.in)) {

			int cases = reader.nextInt();
			for (int num = 0; num < cases; num++) {
				long number = reader.nextLong();
				long number2 = number;
				long number3 = number;
				
				
				int moves = 0;
				int twos = 0;
				int threes = 0;
				while(number2 % 2 == 0 )
				{	
					twos++; 
					number2 /= 2;
				}
				while(number3 % 3 == 0 )
				{	
					threes++; 
					number3 /= 3;
				}
				
				if(number == 1)
				{
					System.out.println("0");
					continue;
				}
				else if(threes < twos )
				{
					System.out.println("-1");
					continue;
				}
				else
				{
					System.out.println(threes + threes - twos);
				}

//				System.out.println("Number:" + number);
//				for (int i = 0; i < 20; i++) {
//					number *= 2;	
//					moves++;
//					
//					 if (Math.log(number)/Math.log(6) - (long)(Math.log(number)/Math.log(6)) < .00000001)
//					 {
//						 System.out.println(Math.log(number)/Math.log(6) + moves );
//					 }
//					
//				}
				
				
				
			}


		}

	}
	
	
}