#include<iostream>
using namespace std;
int n, i, j, a, b, x;
int v[5005];
long long d[5005][5005], s[5005][5005];
int main(){
    cin>> n >> a >> b;
    for(i = 1; i <= n; i++){
        cin>> x;
        v[x] = i;
    }
    for(i = 1; i <= n; i++){
        for(j = 0; j <= n + 1; j++){
            if(j <= v[i]){
                d[i][j] = s[i - 1][j] + b;
            }
            else{
                d[i][j] = s[i - 1][j] + a;
            }
            if(j == v[i]){
                d[i][j] = min(d[i][j], s[i - 1][j - 1]);
            }
            s[i][j] = d[i][j];
            if(j != 0){
                s[i][j] = min(s[i][j], s[i][j - 1]);
            }
        }
    }
    cout<< s[n][n + 1];
}

### Prompt

Your task is to create 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>
using namespace std;
int n, i, j, a, b, x;
int v[5005];
long long d[5005][5005], s[5005][5005];
int main(){
    cin>> n >> a >> b;
    for(i = 1; i <= n; i++){
        cin>> x;
        v[x] = i;
    }
    for(i = 1; i <= n; i++){
        for(j = 0; j <= n + 1; j++){
            if(j <= v[i]){
                d[i][j] = s[i - 1][j] + b;
            }
            else{
                d[i][j] = s[i - 1][j] + a;
            }
            if(j == v[i]){
                d[i][j] = min(d[i][j], s[i - 1][j - 1]);
            }
            s[i][j] = d[i][j];
            if(j != 0){
                s[i][j] = min(s[i][j], s[i][j - 1]);
            }
        }
    }
    cout<< s[n][n + 1];
}

```