#include <iostream>
#include <algorithm>
using namespace std;

long long N, A, B, C[5009];
long long dp[5009][5009];

int main() {
	cin >> N >> A >> B;
	for (int i = 1; i <= N; i++) cin >> C[i];

	for (int i = 0; i <= N; i++) {
		for (int j = 0; j <= N; j++) dp[i][j] = (1LL << 60);
	}
	
	dp[0][0] = 0;
	for (int i = 1; i <= N; i++) {
		long long r = (1LL << 60);
		for (int j = 0; j <= C[i] - 1; j++) r = min(r, dp[i - 1][j]);
		dp[i][C[i]] = r;
		for (int j = 0; j <= C[i] - 1; j++) { dp[i][j] = dp[i - 1][j] + A; }
		for (int j = C[i] + 1; j <= N; j++) { dp[i][j] = dp[i - 1][j] + B; }
	}

	long long ret = (1LL << 60);
	for (int i = 0; i <= N; i++) ret = min(ret, dp[N][i]);
	cout << ret << endl;
	return 0;
}
### Prompt

Your challenge is to write 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
#include <iostream>
#include <algorithm>
using namespace std;

long long N, A, B, C[5009];
long long dp[5009][5009];

int main() {
	cin >> N >> A >> B;
	for (int i = 1; i <= N; i++) cin >> C[i];

	for (int i = 0; i <= N; i++) {
		for (int j = 0; j <= N; j++) dp[i][j] = (1LL << 60);
	}
	
	dp[0][0] = 0;
	for (int i = 1; i <= N; i++) {
		long long r = (1LL << 60);
		for (int j = 0; j <= C[i] - 1; j++) r = min(r, dp[i - 1][j]);
		dp[i][C[i]] = r;
		for (int j = 0; j <= C[i] - 1; j++) { dp[i][j] = dp[i - 1][j] + A; }
		for (int j = C[i] + 1; j <= N; j++) { dp[i][j] = dp[i - 1][j] + B; }
	}

	long long ret = (1LL << 60);
	for (int i = 0; i <= N; i++) ret = min(ret, dp[N][i]);
	cout << ret << endl;
	return 0;
}
```