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

from sys import stdin, stdout  
import math
def primeFactors(n,arr,flgg): 
      
    while n % 2 == 0: 
        arr.append(2) 
        n = n // 2
    
    for i in range(3,int(math.sqrt(n))+1,2):    
        if(i!=3):
            flgg=1
            break
        while n % i== 0:
            arr.append(i) 
            n = n // i 
              
    if n > 2: 
        arr.append(n) 


t=int(stdin.readline())
for _ in range(t):
    n=int(stdin.readline() )
    #x,y,n=(map(int, stdin.readline().strip().split()))
    #arr=list(map(int, stdin.readline() .strip().split()))
    #s=input()

    #stdout.write(str(cp))
    #stdout.write("\n")
    arr=[]
    xx=0
    primeFactors(n,arr,xx)

    tw=0
    th=0
    flg=0
    for i in arr:
        if(i==2):
            tw+=1
        elif(i==3):
            th+=1
        else:
            flg=1

    if(not flg and tw<=th):
        print(th-tw+th)
    else:
        print(-1)
