Score : $400$ points

问题描述

给定一个正整数序列：$A=(a_1,a_2,\ldots,a_N)$。

你可以任意次数（包括零次）选择并执行以下操作之一：

• 选择一个满足 $1 \leq i \leq N$ 且 $a_i$ 是2的倍数的整数 $i$，并将 $a_i$ 替换为 $\frac{a_i}{2}$。
• 选择一个满足 $1 \leq i \leq N$ 且 $a_i$ 是3的倍数的整数 $i$，并将 $a_i$ 替换为 $\frac{a_i}{3}$。

你的目标是使序列 $A$ 满足 $a_1=a_2=\ldots=a_N$。

找出实现目标所需的最小操作总次数。如果无法实现目标，则输出 -1。

以上为通义千问 qwen-max 翻译，仅供参考。

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

update @ 2024/3/10 11:37:21