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 {
    private static Scanner s = new Scanner(System.in);
    public static void main(String[] args) {
	// write your code here

        int t = s.nextInt();
        while(t-->0)
        {
            int n = s.nextInt();

            solve(n);

        }
    }

    private static void solve(int n) {

        if (n == 1)
            System.out.println(0);

        else {
            int cnt3 = 0;
            int cnt2 = 0;
            int temp = n;
            while (temp % 3 == 0) {

                temp /= 3;
                cnt3++;

            }


            while (temp % 2 == 0) {
                temp /= 2;
                cnt2++;

            }
            if (temp != 1) {
                System.out.println(-1);
                return;
            } else {
                if (cnt3 == cnt2) {
                    System.out.println(cnt3);

                } else if (cnt3 > cnt2) {
                    System.out.println((cnt3 - cnt2) + (cnt3));

                } else {
                    System.out.println(-1);
                }


            }


        }

    }

}