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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class code6 {

	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();
		}

		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 void main(String[] args) throws CloneNotSupportedException {
		// TODO Auto-generated method stub
		FastReader scn = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int t = scn.nextInt();
		//int p = t;
		while(t-->0) {
			int n = scn.nextInt();
			int c = 0;
			int flag = 0;
			while(n!=1 && (n*2)%6 == 0) {
				while(n!=1 && n%6 == 0) {
					n/=6;
					c++;
				}
				if(n != 1 && (n*2)%6 != 0)
					flag = 1;
				if(n!=1 && (n*2)%6 == 0) {
					n*=2;
					c++;
				}
			}
			if(flag == 1 || n!=1) {
				System.out.println("-1");
				continue;
			}
			System.out.println(c);
		}
		out.flush();
	}
	
  
	public static boolean check(int mid, int c, int[] arr, int k) {
		int ans = 0;
		for(int i=0; i<arr.length; i++) {
			if(c==0) {
				ans++;
				c = (c+1)%2;
			}else {
				if(arr[i]<=mid) {
					ans++;
					c = (c+1)%2;
				}
			}
		}
		return ans>=k;
	}
	public static int power(int x, int y, int p) 
    { 
        // Initialize result 
        int res = 1;      
         
        // Update x if it is more   
        // than or equal to p 
        x = x % p;  
  
       if (x == 0) return 0; // In case x is divisible by p;    
  
        while (y > 0) 
        { 
            // If y is odd, multiply x 
            // with result 
            if((y & 1)==1) 
                res = (res * x) % p; 
      
            // y must be even now 
            // y = y / 2 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    } 
	
	public static class Pair implements Comparable<Pair>{
		int m;
		int s;
		Pair(int m, int s){
			this.m = m;
			this.s = s; 
		}
		public int compareTo(Pair p) {
			return this.m-p.m;
		}
	}
    
}

