Four Melodies

题意翻译

定义一个 Melody 子序列为，子序列中任意两个相邻元素差为 $1$ 或模 $7$ 同余，这里的子序列不要求连续。 给定一个长度为 $n$ 的序列，求出一种选出 $4$ 个互不相交的 Melody 子序列的方案，使得它们的并的大小尽量大。输出这个大小。 $n \le 3000,a_i \le 10^5$

题目描述

Author note: I think some of you might remember the problem "Two Melodies" from Eductational Codeforces Round 22. Now it's time to make it a bit more difficult! Alice is a composer, and recently she had recorded two tracks that became very popular. Now she has got a lot of fans who are waiting for new tracks. This time Alice wants to form four melodies for her tracks. Alice has a sheet with $ n $ notes written on it. She wants to take four such non-empty non-intersecting subsequences that all of them form a melody and sum of their lengths is maximal. Subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. Subsequence forms a melody when each two adjacent notes either differ by 1 or are congruent modulo 7. You should write a program which will calculate maximum sum of lengths of such four non-empty non-intersecting subsequences that all of them form a melody.

输入输出格式

输入格式

The first line contains one integer number $ n $ ( $ 4<=n<=3000 $ ). The second line contains $ n $ integer numbers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=10^{5} $ ) — notes written on a sheet.

输出格式

Print maximum sum of lengths of such four non-empty non-intersecting subsequences that all of them form a melody.

输入输出样例

输入样例 #1

5
1 3 5 7 9

输出样例 #1

4

输入样例 #2

5
1 3 5 7 2

输出样例 #2

5

说明

In the first example it is possible to compose $ 4 $ melodies by choosing any $ 4 $ notes (and each melody will consist of only one note). In the second example it is possible to compose one melody with $ 2 $ notes — $ {1,2} $ . Remaining notes are used in other three melodies (one note per each melody).