//ΔAGC032D
#include<iostream>
#include<cstdio>
#include<fstream>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<bitset>
#include<cmath>
#include<cstring>
#include<cstdlib>
using namespace std;
typedef long long LL;
typedef double DB;
const int N = 5005;
const LL inf = 1e17;
int n,p[N];
LL a,b,f[N];
int main()
{
	int i,j,o,x,y;
	scanf("%d%d%d",&n,&x,&y);
	a=x,b=y;
	for(i=1;i<=n;i=i+1)
		scanf("%d",p+i);
	p[0]=0,p[n+1]=n+1;
	f[0]=-inf;
	for(i=1;i<=n+1;i=i+1){
		o=-1;
		x=0,y=0;
		for(j=i-1;j>=0;j=j-1){
			if(p[j]>p[i])
				x++;
			else{
				if(p[j]>o){
					f[i]=min(f[i],f[j]+a*x+b*y);
					o=p[j];
				}
				y++;
			}
		}
		//cout<<i<<f[i]+inf<<endl;
	}
	cout<<f[n+1]+inf;
	return 0;
}
### Prompt

Develop a solution in Cpp 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
//ΔAGC032D
#include<iostream>
#include<cstdio>
#include<fstream>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<bitset>
#include<cmath>
#include<cstring>
#include<cstdlib>
using namespace std;
typedef long long LL;
typedef double DB;
const int N = 5005;
const LL inf = 1e17;
int n,p[N];
LL a,b,f[N];
int main()
{
	int i,j,o,x,y;
	scanf("%d%d%d",&n,&x,&y);
	a=x,b=y;
	for(i=1;i<=n;i=i+1)
		scanf("%d",p+i);
	p[0]=0,p[n+1]=n+1;
	f[0]=-inf;
	for(i=1;i<=n+1;i=i+1){
		o=-1;
		x=0,y=0;
		for(j=i-1;j>=0;j=j-1){
			if(p[j]>p[i])
				x++;
			else{
				if(p[j]>o){
					f[i]=min(f[i],f[j]+a*x+b*y);
					o=p[j];
				}
				y++;
			}
		}
		//cout<<i<<f[i]+inf<<endl;
	}
	cout<<f[n+1]+inf;
	return 0;
}
```