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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Set;

public class Contest2 {

    private static void solve(long n) {
        if (n == 1) {
            System.out.println("0");
        }
        if (n % 3 != 0) {
            System.out.println("-1");
            return;
        }
        Set<Long> tried = new HashSet<>();
        long k = 0;
        while (n != 1) {
            k++;
            if (n % 6 == 0) {
                n /= 6;
            } else {
                n *= 2;
            }
            if (tried.contains(n)) {
                System.out.println("-1");
                return;
            }
            tried.add(n);
        }
        System.out.println(k);
    }

    public static void main(String[] args) {
        try {
            BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
            int t = Integer.valueOf(bf.readLine());
            for (int i = 0; i < t; i++) {
                solve(Long.valueOf(bf.readLine()));
            }
        } catch (Exception e) {

        }
    }

}
