#include<bits/stdc++.h>
#define ll long long
#define maxn 5001
#define inf 1000000000000000000
ll p[maxn], pos[maxn], dp[maxn][maxn];
using namespace std;
int main()
{
    ll n, a, b, ans=inf;
    cin>>n>>a>>b;
    for(int i=1; i<=n; i++) cin>>p[i], pos[p[i]]=i;
    memset(dp, 1000000, sizeof dp);
    dp[0][0]=0;
    for(int i=1; i<=n; i++){
        for(int j=0; j<i; j++){
            if(pos[i]>pos[j]){
                dp[i][i]=min(dp[i-1][j], dp[i][i]);
                dp[i][j]=dp[i-1][j]+b;
            }
            else dp[i][j]=dp[i-1][j]+a;
        }
    }
    for(int i=1; i<=n; i++) ans=min(ans, dp[n][i]);
    cout<<ans;
}
### Prompt

Your challenge is to write 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<bits/stdc++.h>
#define ll long long
#define maxn 5001
#define inf 1000000000000000000
ll p[maxn], pos[maxn], dp[maxn][maxn];
using namespace std;
int main()
{
    ll n, a, b, ans=inf;
    cin>>n>>a>>b;
    for(int i=1; i<=n; i++) cin>>p[i], pos[p[i]]=i;
    memset(dp, 1000000, sizeof dp);
    dp[0][0]=0;
    for(int i=1; i<=n; i++){
        for(int j=0; j<i; j++){
            if(pos[i]>pos[j]){
                dp[i][i]=min(dp[i-1][j], dp[i][i]);
                dp[i][j]=dp[i-1][j]+b;
            }
            else dp[i][j]=dp[i-1][j]+a;
        }
    }
    for(int i=1; i<=n; i++) ans=min(ans, dp[n][i]);
    cout<<ans;
}
```