CF818G.Four Melodies

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.

作者注：我想你们中有些人可能还记得 Educational Codeforces Round 22 中的题目“Two Melodies”。现在是时候让它变得更难一点了！

爱丽丝是一位作曲家，最近她录制了两首广受欢迎的乐曲。如今，她拥有了大量期待新作品的粉丝。

这一次，爱丽丝希望为她的乐曲创作四段旋律。

爱丽丝有一张乐谱，上面写有 $n$ 个音符。她希望从中选出四个非空、互不相交的子序列，使得这四个子序列各自都构成一段旋律，并且它们的长度之和最大。

子序列是指通过从原序列中删除若干元素（不改变剩余元素的相对顺序）而得到的序列。

当子序列中任意两个相邻音符之间的差值为 $1$，或二者模 $7$ 同余时，该子序列构成一段旋律。

你需要编写一个程序，计算满足上述条件的四个非空、互不相交子序列的最大长度总和。

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 ≤ 105) — notes written on a sheet.

第一行包含一个整数 $ n $（$ 4 \leq n \leq 3000 $）。

第二行包含 $ n $ 个整数 $ a_1, a_2, \ldots, a_n $（$ 1 \leq a_i \leq 10^5 $）——写在纸上的音符。

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

输出满足以下条件的四个非空、互不相交的子序列的最大长度之和，且这四个子序列各自均构成一段旋律。

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).

在第一个例子中，可以通过选择任意 4 个音符来组成 4 段旋律（每段旋律仅包含一个音符）。

在第二个例子中，可以组成一段包含 2 个音符的旋律——{1, 2}。其余音符则用于另外三段旋律（每段旋律各使用一个音符）。