#include<bits/stdc++.h>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define Reg register
#define RI Reg int
#define Con const
#define CI Con int&
#define I inline
#define W while
#define N 5000
#define LL long long
using namespace std;
int n,A,B,a[N+5];LL f[N+5][N+5];
int main()
{
	RI i,j;for(scanf("%d%d%d",&n,&A,&B),i=1;i<=n;++i) scanf("%d",a+i);
	for(memset(f,63,sizeof(f)),f[0][0]=0,i=1;i<=n;++i)
	{
		for(j=0;j^a[i];++j) f[i][j]=min(f[i][j],f[i-1][j]+A),f[i][a[i]]=min(f[i][a[i]],f[i-1][j]);
		for(j=a[i]+1;j<=n;++j) f[i][j]=min(f[i][j],f[i-1][j]+B);
	}
	LL ans=f[0][1];for(i=0;i<=n;++i) ans=min(ans,f[n][i]);return printf("%lld\n",ans),0;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

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>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define Reg register
#define RI Reg int
#define Con const
#define CI Con int&
#define I inline
#define W while
#define N 5000
#define LL long long
using namespace std;
int n,A,B,a[N+5];LL f[N+5][N+5];
int main()
{
	RI i,j;for(scanf("%d%d%d",&n,&A,&B),i=1;i<=n;++i) scanf("%d",a+i);
	for(memset(f,63,sizeof(f)),f[0][0]=0,i=1;i<=n;++i)
	{
		for(j=0;j^a[i];++j) f[i][j]=min(f[i][j],f[i-1][j]+A),f[i][a[i]]=min(f[i][a[i]],f[i-1][j]);
		for(j=a[i]+1;j<=n;++j) f[i][j]=min(f[i][j],f[i-1][j]+B);
	}
	LL ans=f[0][1];for(i=0;i<=n;++i) ans=min(ans,f[n][i]);return printf("%lld\n",ans),0;
}
```