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 functools
def brute(N):

    @functools.lru_cache(maxsize=N)
    def dfs(n):
        if n == 1:
            return 0
        if n > 6*N:
            return float('inf')
        cands = []
        if n%6 == 0:
            cands.append(1+dfs(n//6))
        cands.append(1+dfs(2*n))
        return min(cands)

    result = dfs(N)
    if result == float('inf'):
        return -1
    return result

def fast1(n):
    # print(n)
    result = float('inf')
    sixpow = 1
    for a in range(32):
        twopow = 1
        for b in range(19):
            # if n == 6**a / 2**b:
            if n == sixpow / twopow:
                print(a,b)
                result = min(result, a+b)
            twopow *= 2
        sixpow *= 6
    if result == float('inf'):
        return -1
    return result

from collections import Counter
def fast(n):
    ctr2 = ctr3 = 0
    while n%2 == 0:
        n//=2
        ctr2+=1
    while n%3 == 0:
        n//=3
        ctr3+=1
    if n != 1:
        return -1
    if ctr2 > ctr3:
        return -1
    return (ctr3 - ctr2) + ctr3

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        
        #CHANGE
        # result = brute(n)
        result = fast(n)

        print(result)

def findPatterns():
    for n in range(1, 1000):
        result = brute(n)
        print(n, result)

def randomTest():
    import random
    # for n in range(10**8, 10**9+1):
    t = 10**4
    for i in range(t):
        n = random.randint(1, 10**9)
        b = brute(n)
        f = fast(n)
        print(n, b, f)
        if b != f:
            print('Broken!')
            return
main()
# findPatterns()
# randomTest()