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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class MultiplyDivide {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        while (t-- > 0) {
            int n = scanner.nextInt();
            int counter = 0;
            int check = 0;
            ArrayList<Integer> list = new ArrayList<>();

            int pos = 0;
            while (true) {
                if (n == 1) {
                    System.out.println(counter);

                    break;
                }
                if (n % 6 == 0) {
                    check = 0;
                    n /= 6;
                } else {
                    if (check > 3) {
                        System.out.println("-1");
                        break;
                    }
                    n *= 2;
                    check++;
                }
                if (list.contains(n)){
                    System.out.println("-1");
                    break;
                }
                list.add(pos, n);
                if (pos >= 6) {
                    pos=0;
                } else {
                    pos++;
                }

                counter++;
            }
        }
    }
}