Problem7389--ABC276 —— D - Divide by 2 or 3

7389: ABC276 —— D - Divide by 2 or 3

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

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 Asatisfy $a_1=a_2=\ldots=a_N$.
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.

Input

The input is given from Standard Input in the following format:
$N$
$a_1\ a_2\ \ldots\ a_N$

Output

Print the answer.

Constraints

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

Sample 1 Input

3
1 4 3

Sample 1 Output

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 2 Input

3
2 7 6

Sample 2 Output

-1
There is no way to achieve the objective.

Sample 3 Input

6
1 1 1 1 1 1

Sample 3 Output

0

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