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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st;
	static PrintWriter out = new PrintWriter(System.out);
	private static final String Y = "YES";
	private static final String N = "NO";

	static void solve() throws Exception {
		int[] pot3 = new int[20];
		pot3[0] = 1;
		for (int i = 1; i < pot3.length; i++) {
			pot3[i] = pot3[i - 1] * 3;
		}
		System.out.println(Arrays.toString(pot3));
		int[] pot2 = new int[31];
		pot2[0] = 1;
		for (int i = 1; i < pot2.length; i++) {
			pot2[i] = pot2[i - 1] * 2;

		}
		System.out.println(Arrays.toString(pot2));
		int tests = nextInt();
		for (int t = 0; t < tests; t++) {
			int n = nextInt();
			int r=0;
			if (n > 1) {
				int p2 = get(n, pot2);
				int p3 = get(n, pot3);
				if (p2 > p3 || p3 < 0) {
					r=-1;
				} else if (p2 == p3) {
					if (n == (pot2[p2] * pot3[p3])) {
						r=p2;
					} else {
						r=-1;
					}
				} else {// p3>p2
					p2 = Math.max(0, p2);
					int dif = p3 - p2;
					r += 2 * dif;
					n /= pot3[dif];
					p3 = p2;
					if (n == (pot2[p2] * pot3[p3])) {
						r+=p2;
					} else {
						r=-1;
					}
				}
			}
			out.println(r);
		}
	}

	private static int get(int val, int[] pots) {
		int r = -1;
		for (int i = pots.length - 1; i > 0; i--) {
			if (val % pots[i] == 0) {
				r = i;
				break;
			}
		}
		return r;
	}

	public static void main(String[] args) throws Exception {
		solve();
		out.close();
	}

	static String next() throws Exception {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(br.readLine());
		}
		return st.nextToken();
	}

	static int nextInt() throws Exception {
		return Integer.parseInt(next());
	}

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