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
import sys
import collections
from collections import defaultdict
from sys import stdin, stdout
MOD = 10**9 + 7


def take_root(num):
    return math.ceil(math.sqrt(num))

def sieve():
    limit = 86028121
    isprime=[1]*(86028122)
    isprime[0]=0
    isprime[1]=0
    for i in range(2,take_root(limit+1)):
        if isprime[i]==1:
            for j in range(i*i,limit+1,i):
                isprime[j]=0
    
    primes=[]
    for i in range(limit+1):
        if isprime[i]==True:
            primes.append(i)
    
    return primes

def minput():
    return map(int,input().split())

def iinput():
    return int(input())

def strinput():
    return input()

def linput():
    return list(map(int,input().split()))

for _ in range(iinput()):
    n=iinput()
    if n==1:
        print(0)
    else:
        temp1 = 0
        while n>0 and n%6==0:
            n=n//6
            temp1+=1
        temp2=0
        while n>0 and n%3==0:
            n=n//3
            temp2+=1
        if n==1:
            print(temp1+(2*temp2))
        else:
            print(-1)