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

# ANSHUL GAUTAM
# IIIT-D

from math import *
from copy import *					# ll = deepcopy(l)
from heapq import *					# heappush(hp,x)
from string import *				# alpha = ascii_lowercase
from random import *				# l.sort(key=lambda l1:l1[0]-l1[1]) => ex: sort on the basis difference
from bisect import *				# bisect_left(arr,x,start,end)  => start and end parameters are temporary
from sys import stdin				# bisect_left return leftmost position where x should be inserted to keep sorted
from sys import maxsize				# minn = -maxsize
from operator import *				# d = sorted(d.items(), key=itemgetter(1))
from itertools import *				# pre = [0] + list(accumulate(l))
from decimal import Decimal 		# a = Decimal(a)	# use this for math questions
from collections import Counter		# d = dict(Counter(l))
from collections import defaultdict # d = defaultdict(list)

'''
7
1
2
3
12
12345
15116544
387420489
'''

def solve(n):
	if(n == 1):
		return 0
	ans = 0
	while(n != 1):
		if(n%3 != 0):
			return -1
		elif(n%6 == 0):
			n //= 6
		else:
			n *= 2
		ans += 1
	return ans
	

T = int(input())
for _ in range(T):
	N = int(stdin.readline())
	print(solve(N))

