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 MultiplyDivide {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		
		int t, n, i, count_three, count_two, number_1, number_2;
		
		Scanner sc = new Scanner(System.in);
		
		t = sc.nextInt();
		
		
		for(i=0; i<t; i++) {
			
			n = sc.nextInt();
			number_1 = n;
			number_2 = n;
			count_three = 0;
			count_two = 0;
			
			if(n == 1)
				System.out.println(0);
			
			else {
			while(number_1 % 3 == 0) {
				number_1 = number_1/3;
				count_three++;
			}
			number_2 = n;
			while(number_2 % 2 == 0) {
				number_2 = number_2/2;
				count_two++;
			}
			
			if((count_two > count_three) | number_1 != 1 | number_2 != 1)
				System.out.println(-1);
			else
				System.out.println(count_two + 2*(count_three-count_two));
			}
		}
		sc.close();
	}

}
