#include <iostream>
#include <vector>
#include <algorithm>
#define INF (1LL<<50LL)

typedef long long ll;

using namespace std;

ll n;
ll a,b;

int main() {
	cin >> n >> a >> b;
	vector<ll> arr(5001);
	vector<ll> dp(5001);
	for(int i = 0; i < n; i++) {
		int p;
		cin >> p;
		arr[p] = i+1;
	}
	for(int num = 1; num <= n; num++) {
		int pos = arr[num];
		ll temp_min = INF;
		for(int i = 0; i <= n; i++) {
			temp_min = min(temp_min,dp[i]);
			if(pos>i) {
				dp[i] = temp_min+b;
			}
			if(pos==i) {
				dp[i] = temp_min;
			}
			if(pos<i) {
				dp[i] = temp_min+a;
			}
			//cout << dp[i] << endl;
		}
		//cout << "-----" << endl;
	}
	ll ans = INF;
	for(int i = 0; i <= n; i++) {
		ans = min(ans,dp[i]);
	}
	cout << ans << endl;
}

### 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 <iostream>
#include <vector>
#include <algorithm>
#define INF (1LL<<50LL)

typedef long long ll;

using namespace std;

ll n;
ll a,b;

int main() {
	cin >> n >> a >> b;
	vector<ll> arr(5001);
	vector<ll> dp(5001);
	for(int i = 0; i < n; i++) {
		int p;
		cin >> p;
		arr[p] = i+1;
	}
	for(int num = 1; num <= n; num++) {
		int pos = arr[num];
		ll temp_min = INF;
		for(int i = 0; i <= n; i++) {
			temp_min = min(temp_min,dp[i]);
			if(pos>i) {
				dp[i] = temp_min+b;
			}
			if(pos==i) {
				dp[i] = temp_min;
			}
			if(pos<i) {
				dp[i] = temp_min+a;
			}
			//cout << dp[i] << endl;
		}
		//cout << "-----" << endl;
	}
	ll ans = INF;
	for(int i = 0; i <= n; i++) {
		ans = min(ans,dp[i]);
	}
	cout << ans << endl;
}

```