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

"""
  ____          _      _____
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| |   / _ \ / _` |/ _ \ |_ / _ \| '__/ __/ _ \/ __|
| |__| (_) | (_| |  __/  _| (_) | | | (_|  __/\__ \
 \____\___/ \__,_|\___|_|  \___/|_|  \___\___||___/

"""
"""
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"""

import sys
import math
import collections
import operator as op
from collections import deque
from math import gcd, inf, sqrt
from bisect import bisect_right, bisect_left

#sys.stdin = open('input.txt', 'r')
#sys.stdout = open('output.txt', 'w')

from functools import reduce
from sys import stdin, stdout, setrecursionlimit
setrecursionlimit(2**20)


def factorial(n):
    if n == 0:
        return 1
    return n * factorial(n - 1)


def ncr(n, r):
    r = min(r, n - r)
    numer = reduce(op.mul, range(n, n - r, -1), 1)
    denom = reduce(op.mul, range(1, r + 1), 1)
    return numer // denom  # or / in Python 2


def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return len(set(factors))


def isPowerOfTwo(x):
    return (x and (not(x & (x - 1))))


def factors(n):
    return list(set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))


def printp(p):
    for i in p:
        print(i)

MOD = 10**9 + 7
T = 1
T = int(stdin.readline())
for _ in range(T):
    #n, k = list(map(int, stdin.readline().split()))
    # s1 = list(stdin.readline().strip('\n'))
    #s = str(stdin.readline().strip('\n'))
    n = int(stdin.readline())
    # a = list(map(int, stdin.readline().split()))
    #x, y, n = list(map(int, stdin.readline().split()))
    flag = True
    ans = 0
    while flag:
        if n == 1:
            break
        elif n % 6 == 0:
            n = n // 6
            ans += 1
        elif n % 3 == 0:
            n = n * 2
            ans += 1
        else:
            flag = False
            break
            
    if flag == False:
        print(-1)
    else:
        print(ans)
