Score : $550$ points

问题描述

设有 $N$ 个袋子排成一行。第 $i$ 个袋子里装有 $x_i$ 日元（日本货币）。

拥有足够资金的高桥和青木轮流执行以下动作：

• 从以下三个动作中选择一个并执行：
  • 选择最左边或最右边的袋子并拿走它。
  • 向 Snuke 支付 $A$ 日元。然后，重复以下动作 $\min(B,n)$ 次（其中 $n$ 是剩余袋子的数量）：选择最左边或最右边的袋子并拿走它。
  • 向 Snuke 支付 $C$ 日元。然后，重复以下动作 $\min(D,n)$ 次（其中 $n$ 是剩余袋子的数量）：选择最左边或最右边的袋子并拿走它。

当所有袋子都被拿走时，定义高桥的收益为“高桥拿走的袋子中的总金额 - 高桥支付给 Snuke 的总金额”；该金额记作 $X$ 日元。类似地，我们定义青木的收益，并用 $Y$ 日元表示这个金额。

若高桥和青木分别采取最优策略以最大化和最小化 $X-Y$，求 $X-Y$ 的值。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

$N$ bags are arranged in a row. The $i$-th bag contains $x_i$ yen (the currency in Japan).

Takahashi and Aoki, who have sufficient money, take alternating turns to perform the following action:

• choose one of the following three actions and perform it.
  • choose the leftmost or rightmost bag and take it.
  • pay $A$ yen to Snuke. Then, repeat the following action $\min(B,n)$ times (where $n$ is the number of the remaining bags): choose the leftmost or rightmost bag and take it.
  • pay $C$ yen to Snuke. Then, repeat the following action $\min(D,n)$ times (where $n$ is the number of the remaining bags): choose the leftmost or rightmost bag and take it.

When all the bags are taken, Takahashi's benefit is defined by "(total amount of money in the bags that Takahashi took) - (total amount of money that Takahashi paid to snuke)"; let this amount be $X$ yen. We similarly define Aoki's benefit, denoting the amount by $Y$ yen.

Find $X-Y$ if Takahashi and Aoki make optimal moves to respectively maximize and minimize $X-Y$.

Constraints

• $1 \leq N \leq 3000$
• $1 \leq x_i \leq 10^9$
• $1 \leq A,C \leq 10^9$
• $1 \leq B,D \leq N$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $A$ $B$ $C$ $D$

$x_1$ $x_2$ $\ldots$ $x_N$

Output

Print the answer.

Sample Input 1

5 10 2 1000000000 1
1 100 1 1 1

Sample Output 1

90

If Takahashi and Aoki make optimal moves, it ends up being $X=92$ and $Y=2$.

Sample Input 2

10 45 3 55 4
5 10 15 20 25 30 35 40 45 50

Sample Output 2

85

Sample Input 3

15 796265 10 165794055 1
18804175 185937909 1934689 18341 68370722 1653 1 2514380 31381214 905 754483 11 5877098 232 31600

Sample Output 3

302361955

update @ 2024/3/10 08:32:30