#include <bits/stdc++.h>

using namespace std;

using ll = long long;
const ll INF = 1e18;

int main() {
   ios_base::sync_with_stdio(false);
   int N; ll tol, tor;
   cin >> N >> tor >> tol;
   vector<int> P(N + 2);
   for (int i = 1; i <= N; ++i) {
      cin >> P[i];
   }
   P[0] = 0;
   P[N + 1] = N + 1;
   vector<ll> dp(N + 2, INF);
   dp[0] = 0;
   for (int i = 1; i <= N + 1; ++i) {
      int cnt = 0;
      for (int j = i - 1; j >= 0; --j) {
         if (P[j] > P[i]) {
            cnt++;
         } else {
            dp[i] = min(dp[i], dp[j] + tor * cnt + tol * (i - j - 1 - cnt));
         }
      }
   }
   cout << dp[N + 1] << "\n";
   return 0;
}

### Prompt

Develop a solution in CPP 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;

using ll = long long;
const ll INF = 1e18;

int main() {
   ios_base::sync_with_stdio(false);
   int N; ll tol, tor;
   cin >> N >> tor >> tol;
   vector<int> P(N + 2);
   for (int i = 1; i <= N; ++i) {
      cin >> P[i];
   }
   P[0] = 0;
   P[N + 1] = N + 1;
   vector<ll> dp(N + 2, INF);
   dp[0] = 0;
   for (int i = 1; i <= N + 1; ++i) {
      int cnt = 0;
      for (int j = i - 1; j >= 0; --j) {
         if (P[j] > P[i]) {
            cnt++;
         } else {
            dp[i] = min(dp[i], dp[j] + tor * cnt + tol * (i - j - 1 - cnt));
         }
      }
   }
   cout << dp[N + 1] << "\n";
   return 0;
}

```