Score : $1000$ points

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.

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 $\{ 1, \ldots, N \}$.

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.

3 20 30
3 1 2

20

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

4 20 30
4 2 3 1

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 $20 + 30 = 50$.

1 10 10
1

0

4 1000000000 1000000000
4 3 2 1

3000000000

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

220