#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
#define fi first
#define se second
typedef pair<ll,ll> P;
#define Mod 1000000007
using VP = vector<P>; using VVP = vector<VP>;
using VI = vector<ll>; using VVI = vector<VI>; using VVVI = vector<VVI>;
#define INF 1ll<<59

int main(){
  ll i,j;
  ll n,a,b;
  cin>>n>>b>>a;
  ll p[n+1];
  for(i=0;i<n;i++) cin>>p[i];
  p[n]=n+1;
  vector<ll> dp(n+1,INF);

  dp[0]=0;
  for(i=1;i<=n;i++){
    ll tmp=0;
    for(j=i-1;j>=0;j--){
      if(p[j]>p[i]) tmp+=b;
      else {
        dp[i]=min(dp[i],dp[j]+tmp);
        tmp+=a;
      }
    }
    dp[i]=min(dp[i],tmp);
  }
  cout<<dp[n]<<endl;
  return 0;
}
### Prompt

Create a solution in CPP for 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;
typedef long long ll;
#define pb push_back
#define fi first
#define se second
typedef pair<ll,ll> P;
#define Mod 1000000007
using VP = vector<P>; using VVP = vector<VP>;
using VI = vector<ll>; using VVI = vector<VI>; using VVVI = vector<VVI>;
#define INF 1ll<<59

int main(){
  ll i,j;
  ll n,a,b;
  cin>>n>>b>>a;
  ll p[n+1];
  for(i=0;i<n;i++) cin>>p[i];
  p[n]=n+1;
  vector<ll> dp(n+1,INF);

  dp[0]=0;
  for(i=1;i<=n;i++){
    ll tmp=0;
    for(j=i-1;j>=0;j--){
      if(p[j]>p[i]) tmp+=b;
      else {
        dp[i]=min(dp[i],dp[j]+tmp);
        tmp+=a;
      }
    }
    dp[i]=min(dp[i],tmp);
  }
  cout<<dp[n]<<endl;
  return 0;
}
```