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.Scanner ;
import java.util.*;
import java.io.*;
import java.math.BigInteger;
import java.nio.IntBuffer;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
//import java.io.OutputStreamReader;
import java.io.PrintWriter;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
//import java.lang.Math;
import java.util.Arrays;
import java.util.Collections;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.InputMismatchException;
 
 
public class cf2{

    public static boolean isPrime(int n) {  
        if (n%2==0){ 
            return false; 
        }
        //if not, then just check the odds 
        for(int i=3;i<=Math.sqrt(n);i+=2) { 
            if(n%i==0){ 
                return false; 
            }
        }
        return true; 
    }

    public static int counttwo(int n){
        int count=0;
        while(n%2==0){
            count++;
            n=n/2;
            //++count;
        }
        return count ;

        
    }
    public static int countthree(int n ){
        int count=0;
        while(n%3==0){
            count++;
            n=n/3;
            //++count;
        }
        return count ;

    }
    public static void main(final String[] args) throws IOException { 
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter w = new PrintWriter(outputStream);

        //ArrayList<Integer> list =new ArrayList<Integer>();
        int t =in.nextInt();
        for(int i=0; i<t; i++){
            int n =in.nextInt();
            String str=Integer.toString(n);
            int ans=0;
            int twocount=0;
            int threecount=0;
            while(n%2==0){
                twocount++;
                n/=2;
            }
            while(n%3==0){
                threecount++;
                n/=3;
            }
            if(n==1){
                if(twocount==0 && threecount==0){
                    System.out.println("0");
                }
                else if (twocount<=threecount){
                    System.out.println((threecount-twocount)+threecount);
                }
                else{
                    System.out.println("-1");
                }
            }
            else {
                System.out.println("-1");
            }
                    
            
        }
    }
}
            
class InputReader {
    private final InputStream stream;
    private final byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private InputReader.SpaceCharFilter filter;
    private final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
 
    public InputReader(final InputStream stream) {
        this.stream = stream;
    }
 
    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
 
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (final IOException e) {
                throw new InputMismatchException();
            }
 
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
 
    public String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (final IOException e) {
            e.printStackTrace();
        }
        return str;
    }
 
    public int nextInt() {
        int c = read();
 
        while (isSpaceChar(c))
            c = read();
 
        int sgn = 1;
 
        if (c == '-') {
            sgn = -1;
            c = read();
        }
 
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
 
        return res * sgn;
    }
 
    public long nextLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
 
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
 
    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E')
                return res * Math.pow(10, nextInt());
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
 
    public String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        final StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
 
        return res.toString();
    }
 
    public boolean isSpaceChar(final int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public String next() {
        return readString();
    }
 
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}