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 solution1():
    for tangocharlie in range(int(input())):
        xx,yy,nn=map(int,input().split())
        p=nn//xx
        k=(p*xx)+yy
        while k>nn:
            p-=1
            k=(p*xx)+yy
        print(k)



def solution2():
    for tangocharlie in range(int(input())):
        nnn=int(input())
        apple=5
        banana=10
        orange=apple+banana
        answer=0
        while nnn>1:
            if nnn%6==0:
                answer+=1
                nnn=nnn//6
            elif nnn%3==0 and nnn%2!=0:
                answer+=1
                nnn*=2
            else:
                answer=-1
                break
        print(answer)


def solution3():
    for tangocharlie in range(int(input())):
        number=int(input())
        sunlight=list(input())
        opnn=wrong=0
        for i in sunlight:
            if i=='(':
                opnn+=1
            else:
                opnn-=1
            
            if opnn<0:
                wrong+=1
                opnn=0
        
        print(wrong)



def solution4():
    for tangocharlie in range(int(input())):
        n,k=map(int,input().split())
        abra_ka_dabra=sorted(list(map(int,input().split())))
        abra_ka_dabra1=[]
        for i in abra_ka_dabra:
            if i%k!=0:
                abra_ka_dabra1.append(k-(i%k))
        if len(abra_ka_dabra1)==0:
            print(0)
            continue
        abra_ka_dabra1.sort()     
        ans=abra_ka_dabra1[0]
        curr=abra_ka_dabra1[0]
        
        for i in range(1,len(abra_ka_dabra1)):
            if abra_ka_dabra1[i]!=abra_ka_dabra1[i-1]:
                curr=abra_ka_dabra1[i]
            else:
                curr+=k
            ans=max(ans,curr)
     
        print(ans+1)
solution2()