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
# prime
def f(n):
    num=n
    d=defaultdict(int)
     
    while n % 2 == 0:
        #print (2),
        d[2]=d[2]+1
        n = n / 2
   
    for i in range(3,4):
      
        while n % i== 0:
            #print (i)
            d[i]=d[i]+1
            n = n / i
 
    #print(d)
    tp=dict(d)
    #print(2**d[2] * 3**d[3],n)
    if 2**d[2] * 3**d[3]!=num:
        return (-1)
    #print("here")
    for i in tp:

        if i not in [2,3]:
            return (-1)
    return [d[2],d[3]] #2,3
    

for tc in range(int(input())):
    #al=list(map(int,input().split()))
    x=int(input())
    a=f(x)
    if type(a)==int:
        print(-1)
    elif a[0]>a[1]:
        print(-1)
    else:
        print(a[0]+2*(a[1]-a[0]))