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.
Output
Print maximum sum of lengths of such two non-empty non-intersecting subsequences that both of them form a melody.
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.