#include <bits/stdc++.h>
#define int long long
using namespace std;

int a[5005];
int dp[5005][5005];
int n,A,B;

int solve(int i, int maxx)
{
    if (i == n) return 0;
    if (dp[i][maxx] != -1) return dp[i][maxx];
    dp[i][maxx] = 0;
    if (a[i + 1] > maxx)
    {
        dp[i][maxx] = min(solve(i + 1, maxx) + A, solve(i + 1, a[i + 1]));
    } else {
        dp[i][maxx] = solve(i + 1, maxx) + B;
    }
    return dp[i][maxx];
}

signed main()
{
    //freopen("file.inp","r",stdin);
    cin >> n >> A >> B;
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i];
        for (int j = 0; j <= n; j++)
        {
            dp[i][j] = -1;
        }
    }
    dp[0][0] = -1;
    cout << solve(0, 0);
    return 0;
}

### Prompt

Please create a solution in cpp 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 int long long
using namespace std;

int a[5005];
int dp[5005][5005];
int n,A,B;

int solve(int i, int maxx)
{
    if (i == n) return 0;
    if (dp[i][maxx] != -1) return dp[i][maxx];
    dp[i][maxx] = 0;
    if (a[i + 1] > maxx)
    {
        dp[i][maxx] = min(solve(i + 1, maxx) + A, solve(i + 1, a[i + 1]));
    } else {
        dp[i][maxx] = solve(i + 1, maxx) + B;
    }
    return dp[i][maxx];
}

signed main()
{
    //freopen("file.inp","r",stdin);
    cin >> n >> A >> B;
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i];
        for (int j = 0; j <= n; j++)
        {
            dp[i][j] = -1;
        }
    }
    dp[0][0] = -1;
    cout << solve(0, 0);
    return 0;
}

```