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.*;

/*
 * To execute Java, please define "static void main" on a class
 * named Solution.
 *
 * If you need more classes, simply define them inline.
 */

public class Solution {
  private static int findOperations(int n){
    int twoCount = 0;
    int threeCount = 0;
    
    while(n%2==0){
      twoCount++;
      n/=2;
    }
    while(n%3==0){
      threeCount++;
      n/=3;
    }
    //System.out.println(twoCount + " " + threeCount);
    if(n != 1) return -1;
    if(twoCount >= threeCount) return threeCount;
    else return 2*threeCount-twoCount;
    
  }
  public static void main(String[] args) {
    //System.out.println(findOperations(387420489));
    Scanner sc = new Scanner(System.in);
    int tests = sc.nextInt();
    
    while(tests > 0){
      int input = sc.nextInt();
      System.out.println(findOperations(input));
      tests--;
    }
    
  }
  
  
}


/* 
Your previous Plain Text content is preserved below:

Idea 
try to find a pattern

1 -> 0
2-> 1
3 -> 2 steps
4 -> -1
5 -> -1
6 ->  1
7 -> -1
8 -> -1
9 -> 


18 * 2 = 36
36/6 = 6
6/6 = 1

3 x 3 * 2

 */