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
# t = int(input())
# for i in range(0,t):
#     a,b,c = list(map(int,input().split()))
#
#
#
#     if (a<c):
#         if (b*a>c):
#             print("1" , b)
#
#         else:
#             print("1 -1")
#
#     else:
#         print("-1 2")




# k = int(input())
# s = 'codeforces'
# val = []
#
# for i in range(0,10):
#     val.append(1)
#
# product = 1
#
# # This below logic is the heart of the problem, how we apply it, and how i code this logic is the king.
# while(product<k):
#
#     for r in range(0,10):
#         val[r]+=1
#         product = product/(val[r]-1)
#         product = product * val[r]
#
#         if product>=k:
#             break
#
#
#
# l = list(s)
# for i in range(0,10):
#     l[i] = l[i]*val[i]
#
#     print(''.join(l[i]),end = "")



t = int(input())


for i in range(0,t):
    n = int(input())

    twos = 0
    threes = 0

    while(n%2==0):
        n = n/2
        twos+=1


    while(n%3==0):
        n = n/3
        threes+=1

    if(n!=1):
        print("-1")

    else:
        if(twos>threes):
            print("-1")
        else:
            print((threes-twos)+threes)

















