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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分