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

#Consistency is the key :)
#code by: amrit2000
from sys import stdin,stdout
import math
input=stdin.readline
def print(x='',y='',end='\n'):
    if y=='':
        stdout.write(str(x)+end)
    else:
        stdout.write(str(x)+' '+str(y)+end)

def solve():
    n=int(input())
    if n==1:
        print(0)
        return

    cnt3,cnt2=0,0
    p=n
    c=0
    while n%6==0:
        n//=6
        c+=1
    if n==1:
        print(c)
        return
    p=n

    while n%3==0:
        n//=3
        cnt3+=1
    if cnt3==0:
        print(-1)
        return
    x=(2**cnt3)*p
    if 6**int(math.log(x,6))!=x:
        print(-1)
        return
    
    
    print(cnt3*2+c)
            
            
        


    
        
tt=1
tt=int(input())
for __ in range(tt):
    solve()
