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

from time import time
from random import randint

def algorithm(n):
    operations = 0
    while (n > 1):
        if n%3 != 0:
            return -1
        if n%6 == 0:
            n //= 6
        else:
            n *= 2
        operations += 1
    return operations

def algorithm2(n):
    cnt2 = cnt3 = 0
    while (n % 2 == 0):
        n //= 2
        cnt2 += 1
    while (n%3 == 0):
        n //= 3
        cnt3 += 1
    if (n == 1 and cnt2 <= cnt3):
        return (2*cnt3 - cnt2)
    else:
        return (-1)


def submit():
    for _ in range(int(input())):
        n = int(input())
        print(algorithm2(n))

def tryOut():
    #start_time = time()
    print(algorithm2(a))
    #print(f"Execution time: {time() - start_time}s")

a = 6
#tryOut()
submit()