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.*;
import java.io.*;

public class B {
	
	static Map<Long, Long> result = new HashMap<Long, Long>();

	public static void main(String args[]) {
		Scanner in = new Scanner(System.in);
		long t = in.nextLong();
		long six = 1;
		long current = 0;
		
		while (six <= 999999999999999999L) {
			result.put(six, current);
			six = six * 6;
			current++;

			// System.out.println(six + " ----- ");

			long two = six;
			long twoC = current;
			while (two % 2 == 0) {
				two = two / 2;
				twoC++;
				
				// System.out.println(two);
				if (result.containsKey(two) == false) {	
					result.put(two, twoC);
				}
			}
		}

		long two = six;
		long twoC = current;
		while (two % 2 == 0) {
			two = two / 2;
			twoC++;
			
			// System.out.println(two);
			if (result.containsKey(two) == false) {	
				result.put(two, twoC);
			}
		}


		// result.forEach((k, v) -> {
		// 	if (v > 28) {
		// 		System.out.println("Key: " + k + " Value: " + v);
		// 	}
		// });


		for (int i  = 0; i < t; i++) {
			long n = in.nextLong();

			solve(n);
		}
	}

	private static void solve(long n) {
		if (result.containsKey(n)) {
			System.out.println(result.get(n));
		} else {
			System.out.println("-1");
		}
	}
}