3158: CF392 - E. Deleting Substrings
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Description
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 ofwand 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 $i\ (l<i<r)$.
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 $w$.
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.
Sample 1 Input
3
0 0 3
1 2 1
Sample 1 Output
3
Sample 2 Input
6
1 4 5 6 7 1000
2 1 1 2 2 3
Sample 2 Output
12