CF813D.Two Melodies

Alice is a beginner composer and now she is ready to create another masterpiece. And not even the single one but two at the same time!

Alice has a sheet with $n$ notes written on it. She wants to take two such non-empty non-intersecting subsequences that both 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 differs by 1 or are congruent modulo 7.

You should write a program which will calculate maximum sum of lengths of such two non-empty non-intersecting subsequences that both of them form a melody.

The first line contains one integer number $n$ ( $2<=n<=5000$ ).

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 two non-empty non-intersecting subsequences that both of them form a melody.

In the first example subsequences $[1,2]$ and $[4,5]$ give length 4 in total.

In the second example subsequences $[62,48,49]$ and $[60,61]$ give length 5 in total. If you choose subsequence $[62,61]$ in the first place then the second melody will have maximum length 2, that gives the result of 4, which is not maximal.