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 math
from collections import defaultdict

def primeFactors(num):
    lis = []
    while num % 2 == 0:
        lis.append(2)
        num = num // 2
    for i in range(3, int(math.sqrt(num)) + 1, 2):
        while num % i == 0:
            if i > 3:
                return []
            lis.append(i)
            num = num // i
    if num > 2:
        lis.append(num)
    return lis


t = int(input())
Dict = defaultdict(list)
for _ in range(t):
    n = int(input())
    if n == 1:
        print(0)
    else:
        if n % 3 != 0:
            print(-1)
        else:
            temp = Dict[n]
            if len(temp) == 0:
                x = primeFactors(n)
                Dict[n] = x
            else:
                x = temp
            if len(x) == 0:
                print(-1)
            else:
                x.sort()
                if x[-1] > 3:
                    print(-1)
                else:
                    two = x.count(2)
                    three = x.count(3)
                    if two > three:
                        print(-1)
                    else:
                        comm = two
                        rem = three - comm
                        print(comm+(rem*2))
