Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tags yet

No tag edit access

E. Deleting Substrings

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSmallR 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*<*r*); - the inequality 2·
*w*_{i}-*w*_{i + 1}-*w*_{i - 1}≥ 0 must hold for all*i*(*l*<*i*<*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.

Input

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*.

Output

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

Examples

Input

3

0 0 3

1 2 1

Output

3

Input

6

1 4 5 6 7 1000

2 1 1 2 2 3

Output

12

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/21/2018 19:32:46 (f2).

Desktop version, switch to mobile version.

User lists

Name |
---|