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 sys
# from math import floor as fl
from math import log
cont = sys.stdin.readlines()
cont = [i.strip('\n') for i in cont]
numTests = int(cont.pop(0)[0])

for i in cont:
    n = int(i)
    if n==1:
        print(0)
        continue
    elif (n%2)%3 == 0 or (n%3)%2 == 0:
        #get the powers of 2
        dupn = n
        num3 = 0
        while dupn % 3 == 0:
            dupn = dupn // 3
            num3 += 1
        num2 = len(bin(dupn)) - 3
        # print(num2,num3)
        # num2 = int(log(2*n // (3**num3) , 2)) - 1
        if 2**num2 * 3**num3 !=n:
            print(-1)
            continue
        if num2 > num3:
            print(-1)
        else:
            print(2*num3 - num2)
    else:
        print(-1)
