/**
 *    author:  tourist
 *    created: 23.03.2019 14:09:32       
**/
#include <bits/stdc++.h>

using namespace std;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  long long A, B;
  cin >> n >> A >> B;
  vector<int> a(n + 2);
  a[0] = 0; a[n + 1] = n + 1;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  vector<long long> dp(n + 2);
  dp[0] = 0;
  for (int i = 1; i <= n + 1; i++) {
    dp[i] = (long long) 1e18;
    int bigger = 0;
    for (int j = i - 1; j >= 0; j--) {
      if (a[j] < a[i]) {
        dp[i] = min(dp[i], dp[j] + bigger * A + (i - 1 - j - bigger) * B);
      } else {
        bigger++;
      }
    }
  }
  cout << dp[n + 1] << '\n';
  return 0;
}

### 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
/**
 *    author:  tourist
 *    created: 23.03.2019 14:09:32       
**/
#include <bits/stdc++.h>

using namespace std;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  long long A, B;
  cin >> n >> A >> B;
  vector<int> a(n + 2);
  a[0] = 0; a[n + 1] = n + 1;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  vector<long long> dp(n + 2);
  dp[0] = 0;
  for (int i = 1; i <= n + 1; i++) {
    dp[i] = (long long) 1e18;
    int bigger = 0;
    for (int j = i - 1; j >= 0; j--) {
      if (a[j] < a[i]) {
        dp[i] = min(dp[i], dp[j] + bigger * A + (i - 1 - j - bigger) * B);
      } else {
        bigger++;
      }
    }
  }
  cout << dp[n + 1] << '\n';
  return 0;
}

```