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 collections
t=int(input())
for _ in range(0,t):
    realn=int(input())
    n = realn
    len3 = 0
    len2 = 0
    if n == 1:
        print(0)
    elif n % 3 != 0:
        print(-1)
    else:
        while n >= 3:
            if n % 3 == 0:
                len3+=1
                n = n // 3
            else:
                break
        while n >= 2:
            if n % 2 == 0:
                len2+=1
                n = n // 2
            else:
                break
        #print("len2:",len2,"len3:",len3)
        if len2 > len3:
            print(-1)
        else:
            multi = len3 - len2
            mul = len3
            for _ in range(0,multi):
                realn *= 2
            for _ in range(0,mul):
                realn //= 6
            #print("n:",n)
            if realn == 1:
                print(multi + mul)
            else:
                print(-1)
        """
        else:
            q=collections.deque()
            q.append([n,0])
            while q:
                #print(q)
                tmp, tried = q.popleft()
                if tmp == 1:
                    print(tried)
                    break
                else:
                    q.append([tmp*2,tried+1])
                    if tmp // 6 != 0:
                        q.append([tmp//6,tried+1])
        """