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 com.company;
import java.util.*;


import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        int t = scanner.nextInt();
        for(int i1 = 0 ;i1<t;i1++){
            int k  = scanner.nextInt();
            int ans = 0;
            int reverlotion = 0;
            while (k!=1){
                if(k%6==0){
                    k/=6;
                    ans++;
                }else {
                    k*=2;
                    ans++;
                }
                reverlotion++;
                if(reverlotion>500){
                    reverlotion = 0;
                    ans = -1;
                    break;
                }
            }
            System.out.println(ans);
        }
    }

    private static Scanner scanner = new Scanner(System.in);
    private static int max(int[] array ){
        int min = Integer.MIN_VALUE;
        for(int i = 0;i< array.length;i++){
            if(array[i]>min){
                min = array[i];
            }
        }
        return min;
    }
    private static int min(int[] array ){
        int min = Integer.MAX_VALUE;
        for(int i = 0;i< array.length;i++){
            if(array[i]<min){
                min = array[i];
            }
        }
        return min;
    }
    private static void readArray(int[] array){
        for(int i = 0;i< array.length;i++){
            array[i] = scanner.nextInt();
        }
    }
    private static void printarray(int[] array){
        for(int i = 0; i< array.length;i++){
            System.out.print(array[i]);
        }
    }
    private static int gcd(int a , int b){
        int k = 0;
        for(int i  =1 ;i<Math.max(a,b);i++){
            if(a%i==0 && b%i==0){
                k = i;
            }
        }
        return k;
    }
    private static int fact(int n){
        if(n==1){
            return 1;
        }
        else {
            return n*fact(n-1);
        }
    }
}