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

T = int(input())
dic = {}
 
def is_2power(K):
    
    if K == 2:
        return True
    
    temp = 2
    
    while(True):
        
        temp *= 2
        
        if temp == K:
            
            return True
        
        if temp > K:
            
            return False
        
        
    
def Fun(num, moves, Mult):
    
    if num in dic:
        
        return dic[num]
        
    temp = num
    
    while(True):
        
        # print(None)
        
        if Mult > 10:
            
            dic[num] = -1
            
            return -1
        
        if temp == 1:
            
            dic[num] = moves
            
            return moves
        
        if temp == 0 or is_2power(temp):
            
            dic[num] = -1
            
            return -1
            
        # print(num)
        
        if (temp % 6) == 0:
            
            temp /=  6
            
            Mult = 0
            
            moves += 1
        
        else:
            
            temp *= 2
            
            Mult += 1
            
            moves += 1
        
     
for i in range(T):
    
    n = int(input())

    print(Fun(n, 0, 0))

# print(dic)
    