#include<bits/stdc++.h>
using namespace std;
#define llong long long
const llong inf=0x3f3f3f3f3f3f3f3f;
int n,A,B;
int nu[5050];
llong f[5050][5050];
int main()
{
    scanf("%d%d%d",&n,&A,&B);
    for(int i=1;i<=n;++i)scanf("%d",&nu[i]);
    memset(f,0x3f,sizeof(f));
    f[0][0]=0;
    int x;
    for(int i=0;i<n;++i)
        for(int j=0;j<=n;++j)
        {
            if(f[i][j]==inf)continue;
            x=nu[i+1];
            if(j>x)f[i+1][j]=min(f[i+1][j],f[i][j]+B);
            else
            {
                f[i+1][x]=min(f[i+1][x],f[i][j]);
                f[i+1][j]=min(f[i+1][j],f[i][j]+A);
            }
        }
    llong ans=inf;
    for(int i=0;i<=n;++i)ans=min(ans,f[n][i]);
    printf("%lld\n",ans);
    return 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>
using namespace std;
#define llong long long
const llong inf=0x3f3f3f3f3f3f3f3f;
int n,A,B;
int nu[5050];
llong f[5050][5050];
int main()
{
    scanf("%d%d%d",&n,&A,&B);
    for(int i=1;i<=n;++i)scanf("%d",&nu[i]);
    memset(f,0x3f,sizeof(f));
    f[0][0]=0;
    int x;
    for(int i=0;i<n;++i)
        for(int j=0;j<=n;++j)
        {
            if(f[i][j]==inf)continue;
            x=nu[i+1];
            if(j>x)f[i+1][j]=min(f[i+1][j],f[i][j]+B);
            else
            {
                f[i+1][x]=min(f[i+1][x],f[i][j]);
                f[i+1][j]=min(f[i+1][j],f[i][j]+A);
            }
        }
    llong ans=inf;
    for(int i=0;i<=n;++i)ans=min(ans,f[n][i]);
    printf("%lld\n",ans);
    return 0;
}

```