Two Melodies
Description
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 a1, a2, ..., an (1 ≤ ai ≤ 105) — 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.
Input
The first line contains one integer number n (2 ≤ n ≤ 5000).
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 two non-empty non-intersecting subsequences that both of them form a melody.
Samples
4
1 2 4 5
4
6
62 22 60 61 48 49
5
Note
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.