#include<bits/stdc++.h>
using namespace std;

typedef long long LL;
const int N=5005;
int pos[N],g[N],a[N];
LL f[N][N],ans;
int n,A,B;

void upmin(LL &x,const LL &y){if(y<x) x=y;}

int main()
{
	scanf("%d%d%d",&n,&A,&B);
	for(int i=1;i<=n;i++) scanf("%d",a+i);
	for(int i=1;i<=n;i++)
	{
		pos[a[i]]=i;
		for(int j=i-1;j;j--)
			if(a[j]>a[i]) g[i]++;
	}
	memset(f,0x3f,sizeof(f));f[0][0]=0;
	for(int i=0,tmp;i<n;i++)
	{
		tmp=pos[i+1];
		for(int j=0;j<=n;j++)
			if(j>g[tmp]) upmin(f[i+1][j-1],f[i][j]+A);
			else upmin(f[i+1][j],f[i][j]+B),upmin(f[i+1][g[tmp]],f[i][j]);
	}
	ans=INT64_MAX;
	for(int i=0;i<=n;i++)
		upmin(ans,f[n][i]);
	printf("%lld\n",ans);
 	return 0;
}
### Prompt

Please formulate a Cpp solution 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<bits/stdc++.h>
using namespace std;

typedef long long LL;
const int N=5005;
int pos[N],g[N],a[N];
LL f[N][N],ans;
int n,A,B;

void upmin(LL &x,const LL &y){if(y<x) x=y;}

int main()
{
	scanf("%d%d%d",&n,&A,&B);
	for(int i=1;i<=n;i++) scanf("%d",a+i);
	for(int i=1;i<=n;i++)
	{
		pos[a[i]]=i;
		for(int j=i-1;j;j--)
			if(a[j]>a[i]) g[i]++;
	}
	memset(f,0x3f,sizeof(f));f[0][0]=0;
	for(int i=0,tmp;i<n;i++)
	{
		tmp=pos[i+1];
		for(int j=0;j<=n;j++)
			if(j>g[tmp]) upmin(f[i+1][j-1],f[i][j]+A);
			else upmin(f[i+1][j],f[i][j]+B),upmin(f[i+1][g[tmp]],f[i][j]);
	}
	ans=INT64_MAX;
	for(int i=0;i<=n;i++)
		upmin(ans,f[n][i]);
	printf("%lld\n",ans);
 	return 0;
}
```