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 os
import random
import re
import sys
import collections
def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n and i<=3:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return factors

def solve():
    for _ in range(int(input())):
        n=int(input())
        if n==1:
            print(0)
            continue
        else:
            l=prime_factors(n)
            c=dict(collections.Counter(l))
            #print(c)
            if 2 not in c and 3 not in c:
                print(-1)
            elif 2 in c and 3 not in c:
                print(-1)
            elif 3 in c and 2 not in c:
                n=n*(2**c[3])
                n=n//(6**c[3])
                if n==1:
                    print(c[3]*2)
                else:
                    print(-1)
            else:
                if c[2]>c[3]:
                    print(-1)
                else:
                    n=n*(2**(c[3]-c[2]))
                    n=n//(6**c[3])
                    if n==1:
                        print((c[3]-c[2])+c[3])
                    else:
                        print(-1)
            
if __name__=="__main__":
    solve()


