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 math
p=int(input())
for i in range(p):
    n=int(input())

    def check(n):
        if n==1:
            return 0
        t=n
        while t%3==0:
            t/=3

        x = math.log(t) / math.log(2)
        if math.floor(x)!=math.ceil(x):
            return -1
        a=n
        while a%6==0:
            a/=6
        y = math.log(a) / math.log(2)
        if math.floor(y)==math.ceil(y):
            return -1

        two=0
        while n%2==0:
            n/=2
            two+=1
        three=math.log(n)/math.log(3)
        q=(2*three - two)
        return '{0:g}'.format(float(q))




    print check(n)