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

    for (int i = 0; i < tests; i++) {
      long number = input.nextInt();

      if (number == 1) {
        answers[i] = 0;
      } else if (number == 6) {
        answers[i] = 1;
      } else if (number < 6) {
        long dist = (long) Math.sqrt(6 / number);
        if (number * Math.pow(2, dist) / 6 == 1) {
          answers[i] = (int) dist + 1;
        } else {
          answers[i] = -1;
        }
      } else if (number > 6) {
        int count = 0;

        while (number >= 6) {
          count++;

          if (number == 0) {
            count = -1;
            break;
          }

          if (number % 6 == 0) {
            number /= 6;
          } else if (number % 6 == 3) {
            number *= 2;
          } else {
            count = -1;
            break;
          }
        }

        if (number == 1) {
          answers[i] = count;
        } else if (number > 0 && number < 6) {
          long dist = (long) Math.sqrt(6 / number);

          if (number * Math.pow(2, dist) / 6 == 1) {
            count += (int) dist + 1;
          } else {
            count = -1;
          }
        }

        answers[i] = count;
      }
    }

    for (int answer : answers) {
      System.out.println(answer);
    }
  }
}
