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, setrecursionlimit
from collections import deque, defaultdict, Counter
import math

rl = lambda: stdin.readline()
rll = lambda: stdin.readline().split()
rli = lambda: map(int, stdin.readline().split())
rlf = lambda: map(float, stdin.readline().split())

INF, NINF = float('inf'), float('-inf')

def solv(n):
	upperlim = 10**9+10
	Q = deque()
	seen = defaultdict(lambda: False)
	layer = 0
	Q.appendleft(n)
	while Q:
		for _ in range(len(Q)):
			curr = Q.pop()
			if seen[curr]: continue
			seen[curr] = True
			if curr == 1:
				return layer
			a = 2*curr
			if a <= upperlim and not seen[a]:
				Q.appendleft(a)
			if curr % 6 == 0 and not seen[curr//6]:
				Q.appendleft(curr//6)
		layer += 1
	return -1

def main():
	T = int(rl())
	for _ in range(T):
		n = int(rl())
		print(solv(n))
	stdout.close()

if __name__ == "__main__":
	main()