Four Melodies
Description
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 a1, a2, ..., an (1 ≤ ai ≤ 105) — 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.
Input
The first line contains one integer number n (4 ≤ n ≤ 3000).
The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105) — notes written on a sheet.
Output
Print maximum sum of lengths of such four non-empty non-intersecting subsequences that all of them form a melody.
Samples
5
1 3 5 7 9
4
5
1 3 5 7 2
5
Note
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).