Problem Statement

You are given a sequence of positive integers: ~A=(a_1,a_2,\ldots,a_N)~ .
You can choose and perform one of the following operations any number of times, possibly zero.

• Choose an integer ~i~ such that ~1 \leq i \leq N~ and ~a_i~ is a multiple of ~2~ , and replace ~a_i~ with ~\frac{a_i}{2}~ .
• Choose an integer ~i~ such that ~1 \leq i \leq N~ and ~a_i~ is a multiple of ~3~ , and replace ~a_i~ with ~\frac{a_i}{3}~ .

Your objective is to make ~A~ satisfy ~a_1=a_2=\ldots=a_N~ .
Find the minimum total number of times you need to perform an operation to achieve the objective. If there is no way to achieve the objective, print -1 instead.

Constraints

• ~2 \leq N \leq 1000~
• ~1 \leq a_i \leq 10^9~
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

~N~

~a_1~ ~a_2~ ~\ldots~ ~a_N~

Output

Print the answer.

Sample Input 1

3
1 4 3

Sample Output 1

3

Here is a way to achieve the objective in three operations, which is the minimum needed.

• Choose an integer ~i=2~ such that ~a_i~ is a multiple of ~2~ , and replace ~a_2~ with ~\frac{a_2}{2}~ . ~A~ becomes ~(1,2,3)~ .
• Choose an integer ~i=2~ such that ~a_i~ is a multiple of ~2~ , and replace ~a_2~ with ~\frac{a_2}{2}~ . ~A~ becomes ~(1,1,3)~ .
• Choose an integer ~i=3~ such that ~a_i~ is a multiple of ~3~ , and replace ~a_3~ with ~\frac{a_3}{3}~ . ~A~ becomes ~(1,1,1)~ .

Sample Input 2

3
2 7 6

Sample Output 2

-1

There is no way to achieve the objective.

Sample Input 3

6
1 1 1 1 1 1

Sample Output 3

0