#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>

#define fo(i,j,l) for(int i=j;i<=l;++i)
#define fd(i,j,l) for(int i=j;i>=l;--i)

using namespace std;
typedef long long ll;
const ll N=5003,M=N<<1,maxn=1e18;

ll f[N];

ll qz[N][N];

int n,p[N];
ll A,B;

inline ll min(ll a,ll b)
{return a<b?a:b;}
inline ll max(ll a,ll b)
{return a>b?a:b;}

int main()
{
	scanf("%d%lld%lld",&n,&A,&B);
	fo(i,1,n)scanf("%d",&p[i]);
	++n; p[n]=n;
	fo(i,1,n){
		qz[i][i]=0;
		fd(l,i-1,1)qz[i][l]=qz[i][l+1]+(p[l]>p[i]);
	}
	p[0]=0;
	fo(i,1,n)f[i]=maxn;
	fo(i,0,n){
		int gs=0;
		fo(l,i+1,n){
			if(gs+qz[l][i+1]==l-i-1&&p[l]>p[i])
			f[l]=min(f[l],f[i]+gs*B+qz[l][i+1]*A);
			gs=gs+(p[l]<p[i]);
		}
	}
	cout<<f[n];
}
### Prompt

Please create a solution in Cpp 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>
#include<cstdio>
#include<cstring>
#include<algorithm>

#define fo(i,j,l) for(int i=j;i<=l;++i)
#define fd(i,j,l) for(int i=j;i>=l;--i)

using namespace std;
typedef long long ll;
const ll N=5003,M=N<<1,maxn=1e18;

ll f[N];

ll qz[N][N];

int n,p[N];
ll A,B;

inline ll min(ll a,ll b)
{return a<b?a:b;}
inline ll max(ll a,ll b)
{return a>b?a:b;}

int main()
{
	scanf("%d%lld%lld",&n,&A,&B);
	fo(i,1,n)scanf("%d",&p[i]);
	++n; p[n]=n;
	fo(i,1,n){
		qz[i][i]=0;
		fd(l,i-1,1)qz[i][l]=qz[i][l+1]+(p[l]>p[i]);
	}
	p[0]=0;
	fo(i,1,n)f[i]=maxn;
	fo(i,0,n){
		int gs=0;
		fo(l,i+1,n){
			if(gs+qz[l][i+1]==l-i-1&&p[l]>p[i])
			f[l]=min(f[l],f[i]+gs*B+qz[l][i+1]*A);
			gs=gs+(p[l]<p[i]);
		}
	}
	cout<<f[n];
}
```