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.