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

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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.

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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 $p = (1, 2, 3)$.

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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 $20 + 30 = 50$.

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Sample Input 3

1 10 10
1

Sample Output 3

0

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Sample Input 4

4 1000000000 1000000000
4 3 2 1

Sample Output 4

3000000000

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Sample Input 5

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

Sample Output 5

220