#include<iostream>
#include<algorithm>
using namespace std;
int n;
long A,B,L[5555],R[5555];
int p[5555];
int main()
{
	cin>>n>>A>>B;
	for(int i=0;i<n;i++)cin>>p[i];
	for(int i=0;i<n;i++)
	{
		long c=0;
		L[i]=9e18;
		for(int j=i;j--;)
		{
			if(p[j]>p[i])
			{
				c+=A;
			}
			else
			{
				L[i]=min(L[i],L[j]+c);
				c+=B;
			}
		}
		L[i]=min(L[i],c);
	}
	for(int i=n;i--;)
	{
		long c=0;
		R[i]=9e18;
		for(int j=i+1;j<n;j++)
		{
			if(p[j]>p[i])
			{
				R[i]=min(R[i],R[j]+c);
				c+=A;
			}
			else
			{
				c+=B;
			}
		}
		R[i]=min(R[i],c);
	}
	long ans=9e18;
	for(int i=0;i<n;i++)ans=min(ans,L[i]+R[i]);
	cout<<ans<<endl;
}
### Prompt

Please create a solution in cpp to the following problem:

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.

Examples

Input

3 20 30
3 1 2


Output

20


Input

4 20 30
4 2 3 1


Output

50


Input

1 10 10
1


Output

0


Input

4 1000000000 1000000000
4 3 2 1


Output

3000000000


Input

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


Output

220

### Response

```cpp
#include<iostream>
#include<algorithm>
using namespace std;
int n;
long A,B,L[5555],R[5555];
int p[5555];
int main()
{
	cin>>n>>A>>B;
	for(int i=0;i<n;i++)cin>>p[i];
	for(int i=0;i<n;i++)
	{
		long c=0;
		L[i]=9e18;
		for(int j=i;j--;)
		{
			if(p[j]>p[i])
			{
				c+=A;
			}
			else
			{
				L[i]=min(L[i],L[j]+c);
				c+=B;
			}
		}
		L[i]=min(L[i],c);
	}
	for(int i=n;i--;)
	{
		long c=0;
		R[i]=9e18;
		for(int j=i+1;j<n;j++)
		{
			if(p[j]>p[i])
			{
				R[i]=min(R[i],R[j]+c);
				c+=A;
			}
			else
			{
				c+=B;
			}
		}
		R[i]=min(R[i],c);
	}
	long ans=9e18;
	for(int i=0;i<n;i++)ans=min(ans,L[i]+R[i]);
	cout<<ans<<endl;
}
```