#include <bits/stdc++.h>
#define int long long 
 
using namespace std;
 
const int maxn = 5000 + 7;
 
int n, A, B, pos[maxn], dp[maxn], a[maxn], ans;
 
int32_t main()
{
    cin >> n >> A >> B;
    for(int i = 1; i <= n; i++)
    {
        cin >> a[i];
    }
    a[n + 1] = 1e15;
    for(int i = 1; i <= n + 1; i++)
    {
        dp[i] = 1e15;
        ans = 0;
        for(int j = i - 1; j >= 0; j--)
        {
            if(a[j] > a[i]) ans++;
            else
            {
                dp[i] = min(dp[i], dp[j] + ans * A + (i - j - 1 - ans) * B);
            }
        }
    }
    cout << dp[n + 1];
}
### Prompt

Construct a cpp code solution to the problem outlined:

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 int long long 
 
using namespace std;
 
const int maxn = 5000 + 7;
 
int n, A, B, pos[maxn], dp[maxn], a[maxn], ans;
 
int32_t main()
{
    cin >> n >> A >> B;
    for(int i = 1; i <= n; i++)
    {
        cin >> a[i];
    }
    a[n + 1] = 1e15;
    for(int i = 1; i <= n + 1; i++)
    {
        dp[i] = 1e15;
        ans = 0;
        for(int j = i - 1; j >= 0; j--)
        {
            if(a[j] > a[i]) ans++;
            else
            {
                dp[i] = min(dp[i], dp[j] + ans * A + (i - j - 1 - ans) * B);
            }
        }
    }
    cout << dp[n + 1];
}
```