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.

The input is given from Standard Input in the following format: >$N$\ >$a_1$ $a_2$ $\ldots$ $a_N$ #### Constraints - $2 \leq N \leq 1000$ - $1 \leq a_i \leq 10^9$ - All values in the input are integers.

Print the answer.

***For Sample #1:*** 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 $(1,1,1)$. ***For Sample #2:*** There is no way to achieve the objective.

AtCoder [ABC276D]