Problem Statement

You are given an integer sequence of length N: $A=(A_1,A_2,\ldots,A_N)$.
You will perform the following consecutive operations just once:

• Choose an integer $x (0\leq x \leq N)$. If x is 0, do nothing. If x is 1 or greater, replace each of $A_1,A_2,\ldots,A_x$ with L.

• Choose an integer $y (0\leq y \leq N)$. If y is 0, do nothing. If y is 1 or greater, replace each of $A_{N},A_{N-1},\ldots,A_{N-y+1}$ with R.

Print the minimum possible sum of the elements of A after the operations.

Input

Input is given from Standard Input in the following format:
N L R
$A_1 A_2 \ldots A_N$

Output

Print the answer.

Constraints

• $1 \leq N \leq 2\times 10^5$
• -$10^9 \leq L, R\leq 10^9$
• -$10^9 \leq A_i\leq 10^9$
• All values in input are integers.

Sample Input 1

5 4 3
5 5 0 6 3

Sample Output 1

14

If you choose x=2 and y=2, you will get A = (4,4,0,3,3), for the sum of 14, which is the minimum sum achievable.

Sample Input 2

4 10 10
1 2 3 4

Sample Output 2

10

If you choose x=0 and y=0, you will get A = (1,2,3,4), for the sum of 10, which is the minimum sum achievable.

Sample Input 3

10 -5 -3
9 -6 10 -1 2 10 -1 7 -15 5

Sample Output 3

-58

L, R, and A_i may be negative.

见题面 Input 部分

见题面 Output 部分