Problem:
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.

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

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		long A = long.Parse(str[1]);
		long B = long.Parse(str[2]);
		long[]P = new long[N];
		long[]P1 = new long[N];
		string[] str2 = Console.ReadLine().Split();
		for(var i=0;i<N;i++){
			P[i] = long.Parse(str2[i]);
			P1[P[i]-1] = i;
		}
		long[,]D = new long[N+1,N*2+1];
		for(var i=1;i<=N;i++){
			long min = D[i-1,0];
			D[i,0] = D[i-1,0]+B;
			for(var j=1;j<N*2+1;j++){
				min = Math.Min(min,D[i-1,j]);
				if(j==P1[i-1]*2+1){
					D[i,j] = min;
				} else if(j%2==1){
					D[i,j] = 99999999999999999;
				} else if(j<P1[i-1]*2+1){
					D[i,j] = min+B;
				} else {
					D[i,j] = min+A;
				}
			}
		}
		long ans = 99999999999999999;
		for(var j=0;j<N*2+1;j++){
			ans = Math.Min(ans,D[N,j]);
		}
		Console.WriteLine(ans);
	}
}