#include <iostream>
#include <stdio.h>
#include <algorithm>

using namespace std;

#define LL long long 
#define FOR(i,l,r) for(int i = l; i <= r; ++i)

const LL oo = 1e18;

LL A,B;
int C[5001],N;
LL F[5001][5001];

void minimize(LL &x,LL y){
    x = min(x,y);
}
void update(int i,int j){
    if(C[i + 1] < C[j]) minimize(F[i + 1][j],F[i][j] + B);
    else{
        minimize(F[i + 1][i + 1],F[i][j]);
        minimize(F[i + 1][j],F[i][j] + A);
    }
}
int main(){

    cin >> N >> A >> B;
    FOR(i,1,N) cin >> C[i];

    FOR(i,1,N) FOR(j,0,i) F[i][j] = oo;

    update(0,0);
    FOR(i,1,N - 1) FOR(j,0,i) if(F[i][j] < oo) update(i,j);

    LL res = oo;
    FOR(i,1,N) res = min(res,F[N][i]);

    cout << res;
    return 0;
}
### Prompt

Please provide a Cpp coded solution 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 <iostream>
#include <stdio.h>
#include <algorithm>

using namespace std;

#define LL long long 
#define FOR(i,l,r) for(int i = l; i <= r; ++i)

const LL oo = 1e18;

LL A,B;
int C[5001],N;
LL F[5001][5001];

void minimize(LL &x,LL y){
    x = min(x,y);
}
void update(int i,int j){
    if(C[i + 1] < C[j]) minimize(F[i + 1][j],F[i][j] + B);
    else{
        minimize(F[i + 1][i + 1],F[i][j]);
        minimize(F[i + 1][j],F[i][j] + A);
    }
}
int main(){

    cin >> N >> A >> B;
    FOR(i,1,N) cin >> C[i];

    FOR(i,1,N) FOR(j,0,i) F[i][j] = oo;

    update(0,0);
    FOR(i,1,N - 1) FOR(j,0,i) if(F[i][j] < oo) update(i,j);

    LL res = oo;
    FOR(i,1,N) res = min(res,F[N][i]);

    cout << res;
    return 0;
}
```