Deleting Substrings

题意翻译

题意 给你一个序列$a$，你每次可以选择一段“山峰形”子串删掉，获得$v$[$length(a)$]的价值，价值可能为负。可以不全删掉，求最大价值。 @yyjr @[chen_zhe](/space/show?uid=8457)

题目描述

SmallR likes a game called "Deleting Substrings". In the game you are given a sequence of integers $ w $ , you can modify the sequence and get points. The only type of modification you can perform is (unexpected, right?) deleting substrings. More formally, you can choose several contiguous elements of $ w $ and delete them from the sequence. Let's denote the sequence of chosen elements as $ w_{l},w_{l+1},...,w_{r} $ . They must meet the conditions: - the equality $ |w_{i}-w_{i+1}|=1 $ must hold for all $ i $ $ (l<=i&lt;r) $ ; - the inequality $ 2·w_{i}-w_{i+1}-w_{i-1}>=0 $ must hold for all $ i $ $ (l&lt;i&lt;r) $ . After deleting the chosen substring of $ w $ , you gain $ v_{r-l+1} $ points. You can perform the described operation again and again while proper substrings exist. Also you can end the game at any time. Your task is to calculate the maximum total score you can get in the game.

输入输出格式

输入格式

The first line contains a single integer $ n $ $ (1<=n<=400) $ — the initial length of $ w $ . The second line contains $ n $ integers $ v_{1},v_{2},...,v_{n} $ $ (0<=|v_{i}|<=2000) $ — the costs of operations. The next line contains $ n $ integers $ w_{1},w_{2},...,w_{n} $ $ (1<=w_{i}<=10^{9}) $ — the initial $ w $ .

输出格式

Print a single integer — the maximum total score you can get.

输入输出样例

输入样例 #1

3
0 0 3
1 2 1

输出样例 #1

3

输入样例 #2

6
1 4 5 6 7 1000
2 1 1 2 2 3

输出样例 #2

12