#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define N 5010
#define inf 1000000000000000ll
int n,A,B; ll f[N][N<<1];
struct data { int x,y; bool operator <(const data&a) const { return x<a.x||x==a.x&&y<a.y; } }a[N];
signed main() {
	scanf("%d%d%d",&n,&A,&B); for (int i=1;i<=n;i++) scanf("%d",&a[i].x),a[i].y=i;
    sort(a+1,a+n+1);
    for (int i=1;i<=n;i++){ll s=inf;for(int j=0;j<=n*2;j++){s=min(s,f[i-1][j]);if(j&1){f[i][j]=s+((j+1>>1)==a[i].y?0:((j+1>>1)<a[i].y?B:A));}else{f[i][j]=s+(((j>>1)<a[i].y?B:A));}}}
    ll ans=inf;
    for (int i=0;i<=n*2;i++) ans=min(ans,f[n][i]);
    cout<<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 ll long long
#define N 5010
#define inf 1000000000000000ll
int n,A,B; ll f[N][N<<1];
struct data { int x,y; bool operator <(const data&a) const { return x<a.x||x==a.x&&y<a.y; } }a[N];
signed main() {
	scanf("%d%d%d",&n,&A,&B); for (int i=1;i<=n;i++) scanf("%d",&a[i].x),a[i].y=i;
    sort(a+1,a+n+1);
    for (int i=1;i<=n;i++){ll s=inf;for(int j=0;j<=n*2;j++){s=min(s,f[i-1][j]);if(j&1){f[i][j]=s+((j+1>>1)==a[i].y?0:((j+1>>1)<a[i].y?B:A));}else{f[i][j]=s+(((j>>1)<a[i].y?B:A));}}}
    ll ans=inf;
    for (int i=0;i<=n*2;i++) ans=min(ans,f[n][i]);
    cout<<ans;
    return 0;
}
```