CF1133E.K Balanced Teams

You are a coach at your local university. There are $n$ students under your supervision, the programming skill of the $i$-th student is $a_i$.

You have to form $k$ teams for yet another new programming competition. As you know, the more students are involved in competition the more probable the victory of your university is! So you have to form no more than $k$ (and at least one) non-empty teams so that the total number of students in them is maximized. But you also know that each team should be balanced. It means that the programming skill of each pair of students in each team should differ by no more than $5$. Teams are independent from one another (it means that the difference between programming skills of two students from two different teams does not matter).

It is possible that some students not be included in any team at all.

Your task is to report the maximum possible total number of students in no more than $k$ (and at least one) non-empty balanced teams.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

你是一所本地大学的编程教练。在你的指导下有 $n$ 名学生，其中第 $i$ 名学生的编程能力为 $a_i$。

你必须为另一场全新的编程竞赛组建 $k$ 支队伍。众所周知，参赛学生人数越多，你所在大学获胜的概率就越高！因此，你需要组建至多 $k$ 支（且至少一支）非空队伍，使得这些队伍中学生总人数尽可能多。但你还知道，每支队伍都必须是“平衡的”：即每支队伍中任意两名学生的编程能力之差至多为 $5$。不同队伍之间相互独立（即来自不同队伍的两名学生的能力差无需满足该限制）。

部分学生可以不被分配到任何队伍中。

你的任务是报告：在至多 $k$ 支（且至少一支）非空平衡队伍的前提下，所能达到的学生总人数的最大值。

如果你使用 Python 编程，在提交代码时请考虑使用 PyPy 而非 Python。

The first line of the input contains two integers $n$ and $k$ ($1 \le k \le n \le 5000$) — the number of students and the maximum number of teams, correspondingly.

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$), where $a_i$ is a programming skill of the $i$-th student.

输入的第一行包含两个整数 $n$ 和 $k$（$1 \le k \le n \le 5000$），分别表示学生的数量和最多可组成的队伍数量。

输入的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le 10^9$），其中 $a_i$ 表示第 $i$ 个学生的编程能力。

Print one integer — the maximum possible total number of students in no more than $k$ (and at least one) non-empty balanced teams.

输出一个整数——在不超过 $k$（且至少为 1）个非空平衡队伍的前提下，学生总数的最大可能值。