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.*;
import java.util.*;

public class Main {
    static Scanner in = new Scanner(System.in);

    public static void main(String[] args) {

        int tc = in.nextInt();
        int k = 0;
        while (k < tc) {
            System.out.println(solve1());
            k++;
        }
    }

    public static void solve2() {

    }

    public static int solve1() {
        int x = in.nextInt();
        HashSet<Integer> set = new HashSet<Integer>();
        int count = 0;
        while (true) {
            if (x == 1) {
                return count;
            }
            if (x / 6 == 0||x%6!=0) {
                count++;
                x = x * 2;
            } else {
                count++;
                x = x / 6;
            }
            if (set.contains(x)) {
                return -1;
            } else {
                set.add(x);
            }
        }

    }
}
