Problem1358--Four Melodies

1358: Four Melodies

Time Limit: 2 Sec  Memory Limit: 256 MB
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Description

time limit per test
5 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

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.

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.

Examples
Input
5
1 3 5 7 9
Output
4
Input
5
1 3 5 7 2
Output
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).

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