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 acmp{
	static Scanner in = new Scanner(System.in);
		// int size = in.nextInt();
		// int[] array = new int[size];
		// for(int i = 0; i<size; i++){
		// 	array[i] = in.nextInt();
		// }

		// int min = Integer.MAX_VALUE;
  		// int max = Integer.MIN_VALUE;
 	
	public static void main(String[] args) {
		//zhan
		//dos
		//md
		int test = in.nextInt();
		while(test>0){
			solve();
			test--;
		}
	}

	public static void solve(){
		int n = in.nextInt();

		int three = 0;
		int two = 0;
		while(n != 1){
			if(n%3 == 0){
				n /= 3;
				three++;
			}else if(n%2 == 0){
				n /= 2;
				two++;			
			}else{
				System.out.println(-1);
				return;
			}
		}
		if(three < two){
			System.out.println(-1);
		}else if(three == two){
			System.out.println(three);
		}else{
			System.out.println(three + (three - two));
		}

	}
}