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

//package codeforces.contest1313.contest1374.B;

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while(t-- > 0) {
            solve(in);
        }
    }

    private static void solve(Scanner in) {
        int x = in.nextInt();
        int original = x;
        if(x == 1) {
            System.out.println(0);
            return;
        }
        int count = 0;

        while(x % 3 == 0) {
            count += 1;
            x /= 3;
        }
        int ans = -1;
        int powersOf2 = f(x);
        if(powersOf2 != -1 && count >= powersOf2) {
            ans = count + (count - powersOf2) + 1;
        }
        System.out.println(ans);
    }

    private static int f(int x) {
        if ((x & (x - 1)) == 0) {
            int count = 0;
            while(x != 0) {
                count += 1;
                x /= 2;
            }
            return count;
        }
        return -1;
    }
}
