Problem Statement

You are given $a permutation p = (p_1, \ldots, p_N)$ of ${ 1, \ldots, N$ }.
You can perform the following two kinds of operations repeatedly in any order:

• Pay a cost A. Choose integers l and $r (1 \leq l < r \leq N)$, and shift $(p_l, \ldots, p_r)$ to the left by one. That is$, replace p_l, p_{l + 1}, \ldots, p_{r - 1}, p_r$ with $p_{l + 1}, p_{l + 2}, \ldots, p_r, p_l,$ respectively.
• Pay a cost B. Choose integers l and $r (1 \leq l < r \leq N)$, and shift $(p_l, \ldots, p_r)$ to the right by one. That is$, replace p_l, p_{l + 1}, \ldots, p_{r - 1}, p_r$ with $p_r, p_l, \ldots, p_{r - 2}, p_{r - 1},$ respectively.

Find the minimum total cost required to sort p in ascending order.

Input

Input is given from Standard Input in the following format:
N A B
$p_1 \cdots p_N$

Output

Print the minimum total cost required to sort p in ascending order.

Constraints

• All values in input are integers.
• $1 \leq N \leq 5000$
• $1 \leq A, B \leq 10^9$
• $(p_1 \ldots, p_N)$ is a permutation of ${ 1, \ldots, N$ }.

Sample Input 1

3 20 30
3 1 2

Sample Output 1

20

Shifting (p_1, p_2, p_3) to the left by one results in p = (1, 2, 3).

Sample Input 2

4 20 30
4 2 3 1

Sample Output 2

50

One possible sequence of operations is as follows:

• Shift (p_1, p_2, p_3, p_4) to the left by one. Now we have p = (2, 3, 1, 4).
• Shift (p_1, p_2, p_3) to the right by one. Now we have p = (1, 2, 3, 4).

Here, the total cost is 20 + 30 = 50.

Sample Input 3

1 10 10
1

Sample Output 3

0

Sample Input 4

4 1000000000 1000000000
4 3 2 1

Sample Output 4

3000000000

Sample Input 5

9 40 50
5 3 4 7 6 1 2 9 8

Sample Output 5

220

见题面 Input 部分

见题面 Output 部分