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

"""
Usage:
    python solution.py < input.txt > solution_output.txt

Testing:
    pytest test_solution.py

Submit:
    Just copy and paste all the code or upload the whole file
"""


def get_input_list() -> str:
    """
    Loops throw the stdio to fetch input data
    Generally used on problems with 'n' inputs

    Returns:
        raw_input_data: The input of a problem
    """
    n = int(input())
    raw_input_data = str(n) + "\n"
    
    for _ in range(n):
        raw_input_data += input() + "\n"
        
    return raw_input_data
    

def get_input() -> str:
    """
    Fetch input data from stdio
    Generally used on problems with discrete inputs
    Returns:
        raw_input_data: The input of a problem
    """
    raw_input_data = ""
    raw_input_data += input()
    return raw_input_data


def multiply_by_two_divide_by_six(n, steps=0):
    if n == 1:
        return steps
    elif int(n % 6) == 0:
        n = int(n / 6)
        return multiply_by_two_divide_by_six(n, steps+1)
    elif int((2 * n) % 6) == 0:
        n = int(n * 2)
        return multiply_by_two_divide_by_six(n, steps+1)
    else:
        return -1
        

def solve(raw_input_data: str):
    """
    Here you solve the problem, happy coding!!
    Args:
        raw_input_data: the data you test the solution

    Returns:
        answer: the solution of the problem
    """
    lines = [int(n) for n in raw_input_data.split()]
    answer = ""
    for n in lines[1:]:
        answer += str(multiply_by_two_divide_by_six(n)) + "\n"
    return str(answer)


if __name__ == "__main__":
    
    while True:
        try:
            # Use this with simple inputs
            # input_data = get_input()
            
            # Use this with the problem have many inputs
            input_data = get_input_list()
            
            answer = solve(input_data)
            print(answer, end="\n")
        except:
            break
