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 final class CodeForces {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while(t-->0) {
            long n = in.nextLong();
            if(Possible(n)) {
                int calc3 = calc3(n);
                int calc2 = calc2(n);
                //System.out.println(calc2 + " " + calc3);
                if(calc2 == calc3)
                    System.out.println(0);
                else if(calc2 > calc3) {
                    System.out.println(-1);
                } else {
                    System.out.println(2 * calc3 - calc2);
                }
            } else {
                System.out.println("-1");
            }
        }
        in.close();
    }

    private static int calc2(long n) {
        int count = 0;
        while(n % 2 == 0) {
            n /= 2;
            count++;
        }
        return count;
    }

    private static int calc3(long n) {
        int count = 0;
        while(n > 0 && n % 3 == 0) {
            n /= 3;
            count++;
        }
        return count;
    }

    private static boolean Possible(long n) {
        while(n % 2 == 0) {
            n /= 2;
        }
        for(int i=3; i<=Math.sqrt(n); i+=2) {
            if(n % i == 0 && i != 3)
                return false;
            while(n % i == 0)
                n /= i;
        }
        if(n > 3)
            return false;
        return true;
    }
}