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.*;

public class Main {
  public static int[] disintergrate(int n) {
    int[] ret = new int[2];

    while (n > 1) {
      if (n % 3 == 0) {
        n /= 3;
        ret[1]++;
      } else if (n % 2 == 0) {
        n /= 2;
        ret[0]++;
      } else
        return null;
    }

    return ret;
  }

  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int t = in.nextInt();

    for (int i = 0; i < t; i++) {
      int n = in.nextInt();

      if (n == 1)
        System.out.println("0");
      else if (n % 2 == 1)
        System.out.println("-1");
      else {
        int[] d = disintergrate(n);

        if (d == null)
          System.out.println("-1");
        else if (d[1] > d[0])
          System.out.println("-1");
        else
          System.out.format("%d\n", d[0]);
      }
    }
  }
}
