#include <bits/stdc++.h>
#define N 5005
#define INF 10000000000000LL
using namespace std;
int n,A,B,p[N],pos[N],cnt[N][N];
long long f[N][N];
int main(){
    scanf("%d%d%d",&n,&A,&B);
    for(int i=1;i<=n;++i){
        scanf("%d",&p[i]);
        pos[p[i]]=i;
    }
    for(int i=n;i;--i)
        for(int j=1;j<=n;++j)
            if(pos[j]>=i)cnt[i][j]=cnt[i+1][j]+(j<=p[i]);
    for(int j=n;j;--j)
        for(int i=n;i;--i)
            if(!cnt[i][j])f[i][j]=f[i][j+1];
            else{
                f[i][j]=min(f[i][j+1]+B,f[pos[j]+1][j+1]+1LL*A*(cnt[i][j]-1));
                //printf("cnt=%d f[%d][%d]=",cnt[i][j]-1,i,j),cout<<f[i][j]<<endl;
            }
    cout<<f[1][1]<<endl;
}

### Prompt

Your task is to create 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>
#define N 5005
#define INF 10000000000000LL
using namespace std;
int n,A,B,p[N],pos[N],cnt[N][N];
long long f[N][N];
int main(){
    scanf("%d%d%d",&n,&A,&B);
    for(int i=1;i<=n;++i){
        scanf("%d",&p[i]);
        pos[p[i]]=i;
    }
    for(int i=n;i;--i)
        for(int j=1;j<=n;++j)
            if(pos[j]>=i)cnt[i][j]=cnt[i+1][j]+(j<=p[i]);
    for(int j=n;j;--j)
        for(int i=n;i;--i)
            if(!cnt[i][j])f[i][j]=f[i][j+1];
            else{
                f[i][j]=min(f[i][j+1]+B,f[pos[j]+1][j+1]+1LL*A*(cnt[i][j]-1));
                //printf("cnt=%d f[%d][%d]=",cnt[i][j]-1,i,j),cout<<f[i][j]<<endl;
            }
    cout<<f[1][1]<<endl;
}

```