#include <bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i, n) for(int i = 0; i < (int)(n); i++)

const int inf = 1000000000000000LL;

int dp[5432];

signed main() {
	int n, a, b;
	cin >> n >> a >> b;
	vector<int> v;
	rep(i, n) {
		int p;
		cin >> p;
		dp[i] = inf;
		int count = 0;
		for(int j = i - 1; j >= 0; j--) {
			if(v[j] < p) {
				dp[i] = min(dp[i], dp[j] + count * a + (i - j - 1 - count) * b);
			}
			if(v[j] > p) {
				count++;
			}
		}
		if(count == i) {
			dp[i] = min(dp[i], count * a);
		}
		v.push_back(p);
	}
	int ans = inf;
	int ma = 0;
	for(int i = n - 1; i >= 0; i--) {
		if(ma < v[i]) {
			ans = min(ans, dp[i] + (n - 1 - i) * b);
		}
		ma = max(ma, v[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;
#define int long long
#define rep(i, n) for(int i = 0; i < (int)(n); i++)

const int inf = 1000000000000000LL;

int dp[5432];

signed main() {
	int n, a, b;
	cin >> n >> a >> b;
	vector<int> v;
	rep(i, n) {
		int p;
		cin >> p;
		dp[i] = inf;
		int count = 0;
		for(int j = i - 1; j >= 0; j--) {
			if(v[j] < p) {
				dp[i] = min(dp[i], dp[j] + count * a + (i - j - 1 - count) * b);
			}
			if(v[j] > p) {
				count++;
			}
		}
		if(count == i) {
			dp[i] = min(dp[i], count * a);
		}
		v.push_back(p);
	}
	int ans = inf;
	int ma = 0;
	for(int i = n - 1; i >= 0; i--) {
		if(ma < v[i]) {
			ans = min(ans, dp[i] + (n - 1 - i) * b);
		}
		ma = max(ma, v[i]);
	}
	cout << ans << endl;
}
```