#include "bits/stdc++.h"
using namespace std;

int main() {
	long long N, A, B, INF = 10000000000000;
	vector<long long> P, DP;
	cin >> N >> A >> B;
	P.resize(N);
	DP.assign(N + 1, INF);
	DP[0] = 0;
	for (int i = 0; i < N; i++) cin >> P[i];
	for (int i = 0; i < N; i++) {
		for (int j = 0; j <= N; j++) {
			if (DP[j] >= INF || j == P[i]) continue;
			if (j < P[i]) {
				DP[P[i]] = min(DP[P[i]], DP[j]);
				DP[j] += A;
			}
			else {
				DP[j] += B;
			}
		}
	}
	long long ANS = INF;
	for (int i = 0; i <= N; i++) {
		ANS = min(ANS, DP[i]);
	}
	cout << ANS << endl;
}
### 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;

int main() {
	long long N, A, B, INF = 10000000000000;
	vector<long long> P, DP;
	cin >> N >> A >> B;
	P.resize(N);
	DP.assign(N + 1, INF);
	DP[0] = 0;
	for (int i = 0; i < N; i++) cin >> P[i];
	for (int i = 0; i < N; i++) {
		for (int j = 0; j <= N; j++) {
			if (DP[j] >= INF || j == P[i]) continue;
			if (j < P[i]) {
				DP[P[i]] = min(DP[P[i]], DP[j]);
				DP[j] += A;
			}
			else {
				DP[j] += B;
			}
		}
	}
	long long ANS = INF;
	for (int i = 0; i <= N; i++) {
		ANS = min(ANS, DP[i]);
	}
	cout << ANS << endl;
}
```