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

a=int(input())
dict_val={1:0,2:-1,3:2,4:-1,5:-1,6:1,7:-1,8:-1,9:4}
for i in range(a):
    val=int(input())
    #dict_val={"2":-1,"3":2,"4":-1,"5":-1,"6":1,"7":-1,"8":-1,"9":4}
    
    #print("Val",val)
    breakval="hi"
    if val<10:
        print(dict_val[val])
    else:
        quo=val
        count_val=int(0)
        count_val2=int(0)
        while quo!=1:
            rem=quo%6
            #print("Rem",rem)
            if rem==0:
                quo=quo//6
                #print("Quo",quo)
                count_val=count_val+1
                #print("count",count_val)
            else:
               break
        while quo!=1:
            rem=quo%3
            #print("Rem",rem)
            if rem==0:
                quo=quo//3
                #print("Quo",quo)
                count_val2=count_val2+1
                #print("count",count_val)
            else:
               break
        if quo==1:
            print(count_val+2*count_val2)
        else:
            print("-1")
            
        
            
        
        
    

        
        
    


