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

########################################

#            SUBTRACTIONS              #

########################################

# for _ in range(int(input())):
#     a, b = map(int, input().split())
#     c = 0
#     while(min(a, b) != 0):
#         ma = max(a, b)
#         mi = min(a, b)
#         a = mi
#         b = ma
#         c += b//a
#         b = b % a
#     print(c)

########################################

#             CANDIES                 #

########################################

# from math import log2, floor, ceil
# for _ in range(int(input())):
#     a = int(input())
#     c = ceil(log2(a))
#     # print(c)
#     for i in range(c, 0, -1):
#         if((a//((2**i)-1)) == ceil(a/((2**i)-1))):
#             print((a//((2**i)-1)))
#             break

########################################

#         VASYA AND SOCKS              #

########################################

# a, b = map(int, input().split())
# c = (a-1)//(b-1)
# print(a+c)

########################################

#       MULTIPLY BY 2, DIVIDE BY 6     #

########################################

for _ in range(int(input())):
    n = int(input())
    if(n == 1):
        print(0)
    else:
        op = 0
        while(True):
            if(n % 6 == 0):
                n = n//6
                op += 1
            elif((n-3) % 6 == 0):
                n = (n*2)//6
                op += 2
            else:
                op = -1
                break
            if(n == 1):
                break
        print(op)
