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

//package src;

import java.util.Scanner;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.StringBuilder;
import java.math.BigInteger;

public class idk {
	static Scanner scn = new Scanner(System.in);
	static int mod = 1000000007;

	public static void main(String args[]) {
		int t = scn.nextInt();
		while (t-- > 0) 
		{
			long  n=scn.nextLong();
			if(n==1)
				System.out.println("0");
			else if(n==6)
				System.out.println("1");
			else if(n==3)
				System.out.println("2");
			else
			{
				if(n%9==0)
				{
					int count=0;
					if(n%6!=0)
					{
						count++;
						n=n*2;
					}
					while(n%6==0)
					{	count++;
						n=n/6;
						//System.out.println(n);
						if(n==1)
							break;
						if(n==9)
						{
							count+=4;
							break;
						}
						
						if(n%6!=0)
						{count++;
							n=n*2;
							
						}
					}
					System.out.println(count);
				}
				else
					System.out.println("-1");
			}
		}

	}
	public static boolean word(String arr[],String str,String ori,HashMap<String, Integer>map,int i,int j)
	{	if(j==str.length())
	{	//System.out.println(str);
		if(str.length()==0)
			return true;
		else
			return false;
	}
		
		String re=ori.substring(i,j);
		System.out.println(re);
		if(map.containsKey(re))
		{	String res=ori.substring(j);
		
			return word(arr, str,ori, map, j, j);
		}
		
			return word(arr, str,ori, map, i, j+1);
			
		
	}
	public static int decode(String str, int i, int[] memo) {
		if (i == 0) {
			return 1;
		}
		int ind = str.length() - i;
		if (str.charAt(ind) == '0')
			return 0;
		if (memo[i] != -1)
			return memo[i];
		int res = decode(str, i - 1, memo);
		if (i >= 2 && Integer.parseInt(str.substring(ind, ind + 2)) <= 26) {
			res += decode(str, i - 2, memo);
		}
		memo[i] = res;
		return res;
	}

	public static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	public static String factorial(int n) {
		BigInteger fac = new BigInteger("1");
		for (int i = 1; i <= n; i++) {
			fac = fac.multiply(BigInteger.valueOf(i));
		}
		return fac.toString();
	}

}

class pair {
	int a;
	int b;

	pair(int x, int y) {
		this.a = x;
		this.b = y;
	}
}

class sorting implements Comparator<pair> {

	@Override
	public int compare(pair o1, pair o2) {
		// TODO Auto-generated method stub
		int x=o1.a-o2.a,y=o1.b-o2.b;
		if(y==0)
		{
			if(x>=0)
				return -1;
				else
					return 1;
		}
		else if(y>0)
			return -1;
		else
			return 1;
	}

}
