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.

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.

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

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).