CF1201A.Important Exam

A class of students wrote a multiple-choice test.

There are $n$ students in the class. The test had $m$ questions, each of them had $5$ possible answers (A, B, C, D or E). There is exactly one correct answer for each question. The correct answer for question $i$ worth $a_i$ points. Incorrect answers are graded with zero points.

The students remember what answers they gave on the exam, but they don't know what are the correct answers. They are very optimistic, so they want to know what is the maximum possible total score of all students in the class.

一个班级的学生参加了一次多项选择题测试。

班级中共有 $n$ 名学生。测试共有 $m$ 道题目，每道题均有 $5$ 个可能的答案（A、B、C、D 或 E）。每道题有且仅有一个正确答案。第 $i$ 题的正确答案值 $a_i$ 分。答错不得分。

学生们记得自己在考试中给出的答案，但不知道各题的正确答案。他们非常乐观，因此希望知道全班学生可能获得的最高总分。

The first line contains integers $n$ and $m$ ($1 \le n, m \le 1000$) — the number of students in the class and the number of questions in the test.

Each of the next $n$ lines contains string $s_i$ ($|s_i| = m$), describing an answer of the $i$-th student. The $j$-th character represents the student answer (A, B, C, D or E) on the $j$-th question.

The last line contains $m$ integers $a_1, a_2, \ldots, a_m$ ($1 \le a_i \le 1000$) — the number of points for the correct answer for every question.

第一行包含两个整数 $n$ 和 $m$（$1 \le n, m \le 1000$）—— 分别表示班级中的学生人数和测试中的题目数量。

接下来的 $n$ 行中，每行包含一个字符串 $s_i$（$|s_i| = m$），表示第 $i$ 个学生的作答情况。其中第 $j$ 个字符表示该学生对第 $j$ 道题的回答（A、B、C、D 或 E）。

最后一行包含 $m$ 个整数 $a_1, a_2, \ldots, a_m$（$1 \le a_i \le 1000$）—— 表示每道题答对时所获得的分数。

Print a single integer — the maximum possible total score of the class.

输出一个整数——班级可能获得的最高总分。

In the first example, one of the most optimal test answers is "ABCD", this way the total number of points will be $16$.

In the second example, one of the most optimal test answers is "CCC", this way each question will be answered by exactly one student and the total number of points is $5 + 4 + 12 = 21$.

在第一个例子中，一种最优的测试答案是“ABCD”，此时总得分为 $16$。

在第二个例子中，一种最优的测试答案是“CCC”，此时每个问题恰好被一名学生答对，总得分为 $5 + 4 + 12 = 21$。