#include "iostream"
#include "vector"

using namespace std;

int main(){
	int N,L,R;
	cin>>N>>R>>L;
	vector<int>v(N);
	for(auto &i:v)cin>>i;
	vector<int>place(N+1);
	for(int i=0;i<N;i++){
		place[v[i]]=i;
	}
	vector<vector<long long int>>dp(2,vector<long long int>(N+2));
	for(int i=1;i<=N;i++){
		int index =i&1;
		long long int box=dp[index^1][0];
		for(int j=0;j<=N+1;j++){
			box=min(box,dp[index^1][j]);
			if(place[i]+1>j)dp[index][j]=box+L;
			else if(place[i]+1==j)dp[index][j]=box;
			else dp[index][j]=box+R;
		}
	}
	long long int ans=1000000000000000000;
	for(int i=0;i<=N+1;i++)ans=min(ans,dp[N&1][i]);
	cout<<ans<<endl;
}
### Prompt

Please formulate 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 "vector"

using namespace std;

int main(){
	int N,L,R;
	cin>>N>>R>>L;
	vector<int>v(N);
	for(auto &i:v)cin>>i;
	vector<int>place(N+1);
	for(int i=0;i<N;i++){
		place[v[i]]=i;
	}
	vector<vector<long long int>>dp(2,vector<long long int>(N+2));
	for(int i=1;i<=N;i++){
		int index =i&1;
		long long int box=dp[index^1][0];
		for(int j=0;j<=N+1;j++){
			box=min(box,dp[index^1][j]);
			if(place[i]+1>j)dp[index][j]=box+L;
			else if(place[i]+1==j)dp[index][j]=box;
			else dp[index][j]=box+R;
		}
	}
	long long int ans=1000000000000000000;
	for(int i=0;i<=N+1;i++)ans=min(ans,dp[N&1][i]);
	cout<<ans<<endl;
}
```