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

#define int long long

const int N = 5e3 + 10, INF = 1e15 + 10;
int n, A, B, ans = INF, ar[N], dp[N];

int32_t main() {
	cin >> n >> A >> B;
	for (int i = 0; i < n; i++)
		cin >> ar[i];
	
	for (int i = 0; i < n; i++) 
		for (int j = 0; j < i; j++)
			if (ar[j] > ar[i])
				dp[i] += A;
			else
				dp[i] += B;
	
	for (int i = 1; i < n; i++) {
		int sum = 0;
		for (int j = i - 1; j >= 0; j--) {
			if (ar[j] < ar[i])
				dp[i] = min(dp[i], dp[j] + sum);
			
			if (ar[j] > ar[i])
				sum += A;
			else
				sum += B;
		}
	}
	
	for (int i = 0; i < n; i++) {
		int sum = 0;
		for (int j = i + 1; j < n; j++)
			if (ar[j] < ar[i])
				sum += B;
			else
				sum += A;
		ans = min(ans, sum + dp[i]);
	}
	cout << ans;
}
### Prompt

Generate 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 <bits/stdc++.h>
using namespace std;

#define int long long

const int N = 5e3 + 10, INF = 1e15 + 10;
int n, A, B, ans = INF, ar[N], dp[N];

int32_t main() {
	cin >> n >> A >> B;
	for (int i = 0; i < n; i++)
		cin >> ar[i];
	
	for (int i = 0; i < n; i++) 
		for (int j = 0; j < i; j++)
			if (ar[j] > ar[i])
				dp[i] += A;
			else
				dp[i] += B;
	
	for (int i = 1; i < n; i++) {
		int sum = 0;
		for (int j = i - 1; j >= 0; j--) {
			if (ar[j] < ar[i])
				dp[i] = min(dp[i], dp[j] + sum);
			
			if (ar[j] > ar[i])
				sum += A;
			else
				sum += B;
		}
	}
	
	for (int i = 0; i < n; i++) {
		int sum = 0;
		for (int j = i + 1; j < n; j++)
			if (ar[j] < ar[i])
				sum += B;
			else
				sum += A;
		ans = min(ans, sum + dp[i]);
	}
	cout << ans;
}
```