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

def get_arry():
    return list(map(int,input().split()))
def get_int():
    return int(input())
def get_input():
    return input()
def areParanthesisBalanced(expr) :
    stack = []

    for char in expr:
        if char in ["(", "{", "["]:

            stack.append(char)
        else:

            if not stack:
                return False
            current_char = stack.pop()
            if current_char == '(':
                if char != ")":
                    return False
            if current_char == '{':
                if char != "}":
                    return False
            if current_char == '[':
                if char != "]":
                    return False

    # Check Empty Stack
    if stack:
        return False
    return True

def main():
    for _ in range(int(input())):
        n=get_int()
        cnt=0
        flag=0
        if n==1:
            print(0)
        else:
            while n!=1:
                if n%6==0:
                    n=n//6
                else:
                    if (n*2)%6!=0:
                        print(-1)
                        flag=1
                        break
                    else:
                        n=n*2

                cnt+=1
            if flag==0 and cnt!=0:
                print(cnt)
            elif flag==0 and cnt==0:
                print(-1)


if __name__ == '__main__':
    main()
