#include <bits/stdc++.h>
#define N 5002
using namespace std;
long long n,a,b,i,j,f[N],sl,ma,p[N];
int main()
{
   // freopen("ntu.inp","r",stdin);
   // freopen("ntu.out","w",stdout);
    cin>>n>>a>>b;
    for(i=1;i<=n;i++) cin>>p[i];
    p[n+1]=n+1;
    for(i=1;i<=n+1;i++)
    {
        ma=-1; sl=0; f[i]=round(1e18);
        for(j=i-1;j>=0;j--)
            if(p[j]>p[i]) sl++;
            else
            {
                if(ma<p[j]) f[i]=min(f[i],f[j]+sl*a+(i-j-1-sl)*b);
                ma=max(ma,p[j]);
            }
    }
    cout<<f[n+1];
}

### Prompt

In cpp, your task is to solve 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 5002
using namespace std;
long long n,a,b,i,j,f[N],sl,ma,p[N];
int main()
{
   // freopen("ntu.inp","r",stdin);
   // freopen("ntu.out","w",stdout);
    cin>>n>>a>>b;
    for(i=1;i<=n;i++) cin>>p[i];
    p[n+1]=n+1;
    for(i=1;i<=n+1;i++)
    {
        ma=-1; sl=0; f[i]=round(1e18);
        for(j=i-1;j>=0;j--)
            if(p[j]>p[i]) sl++;
            else
            {
                if(ma<p[j]) f[i]=min(f[i],f[j]+sl*a+(i-j-1-sl)*b);
                ma=max(ma,p[j]);
            }
    }
    cout<<f[n+1];
}

```