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.*;
import java.util.*;

public class Main{

    public static void main(String commandLineArgument[]){

        FS input = new FS();
        PrintWriter out = new PrintWriter(System.out);
        int tc = input.nextInt();
        while(tc --> 0){
            long n = input.nextLong();
            int twoCount = 0 , threeCount = 0 , answerExist = 0;
            while(n > 1){
                if(n % 2 == 0){
                    n /= 2;
                    ++twoCount;
                }
                else
                if(n % 3 == 0){
                    n /= 3;
                    ++threeCount;
                }
                else {
                    answerExist = -1;
                    break;
                }
            }
            if(answerExist != -1){
                answerExist = threeCount + (threeCount - twoCount);
                if(twoCount > threeCount){
                    answerExist = -1;
                }
            }
            out.println(answerExist);
        }
        out.close();
    }
}
class FS{
    BufferedReader br;
    StringTokenizer st;
    public FS() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    String next() {
        while(st == null || !st.hasMoreElements()) {
            try {st = new StringTokenizer(br.readLine());}
            catch(Exception e) { throw null;}
        }
        return st.nextToken();
    }
    int nextInt() { return Integer.parseInt(next());}
    double nextDouble() { return Double.parseDouble(next());}
    long nextLong() { return Long.parseLong(next());}
    int[] NIA(int n) {
        int r[] = new int[n];
        for(int i = 0; i < n; i++) r[i] = nextInt();
        return r;
    }
    long[] NLA(int n) {
        long r[] = new long[n];
        for(int i = 0; i < n; i++) r[i] = nextLong();
        return r;
    }
    char[][] grid(int r, int c){
        char res[][] = new char[r][c];
        for(int i = 0; i < r; i++) {
            char l[] = next().toCharArray();
            for(int j = 0; j < c; j++) {
                res[i][j] = l[j];
            }
        }
        return res;
    }
}