A11009. Four Melodies
编程题
普及/提高-
知识点
题目描述
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.
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.
输入格式
The first line contains one integer number $n$ ( $4<=n<=3000$ ).
The second line contains $n$ integer numbers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{5}$ ) — notes written on a sheet.
The second line contains $n$ integer numbers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{5}$ ) — notes written on a sheet.
输出格式
Print maximum sum of lengths of such four non-empty non-intersecting subsequences that all of them form a melody.
输入输出样例
输入 #1
5 1 3 5 7 9
输出 #1
4
输入 #2
5 1 3 5 7 2
输出 #2
5
说明/提示
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).
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).