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

"""
Given an integer n

In one move you can either:
    multiply by 2
    or divide by 6 (if div by 6)

Given a number n determine the minimum number of moves required to get it to 1
If it is impossible print -1

This is only possible if n has factors 2 and 3
This is also only possible if there are more factors of 3 than 2
And the answer is given by the deficit of 2s to 3s + log(result)
"""


def check(n):
    if n == 1:
        return 0

    # Count how many factors of 2 and 3 it has
    two_count, three_count = 0, 0

    while n % 2 == 0:
        n /= 2
        two_count += 1

    while n % 3 == 0:
        n /= 3
        three_count += 1

    if two_count > three_count:
        return -1

    if n != 1:  # If its factors are only 2 and 3 then it should only be 1
        return -1

    times_2 = three_count - two_count
    div_6 = three_count

    return times_2 + div_6


t = int(input())

for i in range(t):
    n = int(input())
    print(check(n))


