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.*;
import java.lang.*;
import java.math.BigInteger;

public class hello {
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException  e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
	public static FastReader sc = new FastReader();
	public static void take_array(long arr[], int size) {
		for (int i = 0; i < size; i++) {
			arr[i] = sc.nextLong();
		}
	}
	public static void print_arr(long arr[]) {
		for (long x : arr)
			System.out.print(x + " ");
	}
	public static String[] convert_String_to_arr(String s) {
		String arr[] = new String[s.length()];
		for (int i = 0; i < s.length(); i++) {
			arr[i] = String.valueOf(s.charAt(i));
		}
		return arr;
	}
	public static void take_prefix_array(long arr[], int size, long []prefix) {
		long temp = 0;
		for (int i = 0; i < size; i++) {
			temp += arr[i];
			prefix[i] = temp;
		}
	}
	public static void print(Object c, int a) {
		if (a == -1)
			System.out.print(c + " ");
		else
			System.out.println(c);
	}
	public static void space() {
		System.out.println();
	}
	public static long sum_array(long arr[]) {
		long sum = 0;
		for (long x : arr)
			sum += x;
		return sum;
	}
	public static void swap(long a, long b) {
		long temp = a;
		a = b;
		b = temp;
	}
	public static long min(long a, long b, long c) {
		return Math.min(a, Math.min(b, c));
	}
	public static long max(long a, long b, long c) {
		return Math.max(a, Math.max(b, c));
	}
	public static long gcd(long a, long b) {
		if (a < b)swap(a, b);
		if (b == 0)return a;
		return gcd(b, a % b);
	}
	public static void main(String[] args)throws IOException {
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int count2 = 0, count3 = 0;
			while (n % 2 == 0) {
				count2++;
				n /= 2;
			}
			while (n % 3 == 0) {
				count3++;
				n /= 3;
			}
			if (n == 1 && count2 <= count3)
				System.out.println(2 * count3 - count2);
			else
				System.out.println("-1");
		}
	}

}