#include<bits/stdc++.h>

using namespace std;
#define ll long long
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define all(vr) vr.begin(),vr.end()
const ll N=1e5+10,inf=1e18;
ll dp[N],p[N],n,A,B;
int main()
{
    //freopen("ss.inp","r",stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>n>>A>>B;
    for (int i=1;i<=n;i++) cin>>p[i],dp[i]=inf;
    dp[n+1]=inf;
    p[n+1]=n+1;
    for (int i=0;i<=n;i++)
    {
        ll cnt=0;
        for (int j=i+1;j<=n+1;j++)
            if (p[j]>p[i]) dp[j]=min(dp[j],dp[i]+(j-i-1-cnt)*A+cnt*B);
            else cnt++;
    }
    cout<<dp[n+1];
    return 0;
}

### 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<bits/stdc++.h>

using namespace std;
#define ll long long
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define all(vr) vr.begin(),vr.end()
const ll N=1e5+10,inf=1e18;
ll dp[N],p[N],n,A,B;
int main()
{
    //freopen("ss.inp","r",stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>n>>A>>B;
    for (int i=1;i<=n;i++) cin>>p[i],dp[i]=inf;
    dp[n+1]=inf;
    p[n+1]=n+1;
    for (int i=0;i<=n;i++)
    {
        ll cnt=0;
        for (int j=i+1;j<=n+1;j++)
            if (p[j]>p[i]) dp[j]=min(dp[j],dp[i]+(j-i-1-cnt)*A+cnt*B);
            else cnt++;
    }
    cout<<dp[n+1];
    return 0;
}

```