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.File;
import java.io.FileNotFoundException;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {
//		Scanner reader = new Scanner(new File("b.in"));
		Scanner reader = new Scanner(System.in);
		
		int numCases = Integer.valueOf(reader.nextLine());
		
		for(int i = 0; i < numCases; i++) {
			int n = Integer.valueOf(reader.nextLine());
			
			if(n == 1) {
				System.out.println(0);
			} else if(n % 3 != 0) {
				System.out.println(-1);
			} else {
				double a = (double) n;
				int t = 0;
				
				while(true) {
					if(a % 6 == 0) {
						a /= 6;
						t++;
					} else if(Math.log(a)/Math.log(3) % 1 == 0) {
						
						System.out.println(getNumSteps((long) n));
						
						break;
					} else {
						System.out.println(-1);
						break;
					}
				}
			}
			
		} 
	}
	
	private static int getNumSteps(long n) {
		int i = 0;
		
		while(true) {
//			if(Math.log(n)/Math.log(6) % 1 == 0) {
//				i += Math.log(n)/Math.log(6);
//				break;
//			} else if(n % 6 == 0) else {
//				n *= 2;
//				i++;
//			}
			if(n == 1) {
				break;
			} if(n % 6 == 0) {
				n /= 6;
				i += 1;
			} else {
				n *= 2;
				i++;
			}
		}
		
		return i;
	}
}