#include <bits/stdc++.h>

using namespace std;

using LL = long long;

int n, a, b;
LL dp[5005][5005];
int arr[5005], pos[5005], cnt[5005];

int main() {
	scanf("%d%d%d", &n, &a, &b);
	for (int i = 1; i <= n; ++i) {
		scanf("%d", arr + i);
		pos[arr[i]] = i;
	}
	memset(dp, 0x3f, sizeof(dp));
	for (int i = 0; i <= n; ++i) dp[0][i] = dp[i][0] = 0;
	for (int i = 1; i <= n; ++i) {
		for (int j = arr[i] + 1; j <= n; ++j)
			if (pos[j] < i) ++cnt[j];
		for (int j = 1; j <= n; ++j)
			if (pos[j] <= i) {
				if (cnt[j] == 0)
					dp[i][j] = dp[i][j - 1];
				else
					dp[i][j] = min(dp[i][j - 1] + a, dp[pos[j] - 1][j] + 1LL * b * cnt[j]);
			} else {
				dp[i][j] = dp[i][j - 1];
			}
	}
	printf("%lld\n", dp[n][n]);
}
### Prompt

Please create a solution in Cpp 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;

using LL = long long;

int n, a, b;
LL dp[5005][5005];
int arr[5005], pos[5005], cnt[5005];

int main() {
	scanf("%d%d%d", &n, &a, &b);
	for (int i = 1; i <= n; ++i) {
		scanf("%d", arr + i);
		pos[arr[i]] = i;
	}
	memset(dp, 0x3f, sizeof(dp));
	for (int i = 0; i <= n; ++i) dp[0][i] = dp[i][0] = 0;
	for (int i = 1; i <= n; ++i) {
		for (int j = arr[i] + 1; j <= n; ++j)
			if (pos[j] < i) ++cnt[j];
		for (int j = 1; j <= n; ++j)
			if (pos[j] <= i) {
				if (cnt[j] == 0)
					dp[i][j] = dp[i][j - 1];
				else
					dp[i][j] = min(dp[i][j - 1] + a, dp[pos[j] - 1][j] + 1LL * b * cnt[j]);
			} else {
				dp[i][j] = dp[i][j - 1];
			}
	}
	printf("%lld\n", dp[n][n]);
}
```