#include<cstdio>
#include<algorithm>
#include<cstring>
#define LL long long
using namespace std;
const int maxn = 5e3 + 5;
LL f[maxn], mn, ans;
int a[maxn], n, A, B, pos[maxn];
int main() {
	scanf("%d%d%d", &n, &A, &B);
	for(register int i = 1; i <= n; ++i) 
		scanf("%d", &a[i]), pos[a[i]] = i;
	memset(f, 0x3f, sizeof(f)), f[0] = 0;
	ans = 0x3f3f3f3f3f3f3f3f;
	for(register int i = 1; i <= n; ++i) {
		mn = 0x3f3f3f3f3f3f3f3f;
		for(register int j = 0; j <= n; ++j) {
			mn = min(mn, f[j]);
			if(pos[i] < j) f[j] = mn + A;
			else if(pos[i] > j) f[j] = mn + B;
			else f[j] = mn;
		}
	}
	for(register int i = 1; i <= n; ++i)
		ans = min(f[i], ans);
	printf("%lld", ans);
	return 0;
} 
### 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<cstdio>
#include<algorithm>
#include<cstring>
#define LL long long
using namespace std;
const int maxn = 5e3 + 5;
LL f[maxn], mn, ans;
int a[maxn], n, A, B, pos[maxn];
int main() {
	scanf("%d%d%d", &n, &A, &B);
	for(register int i = 1; i <= n; ++i) 
		scanf("%d", &a[i]), pos[a[i]] = i;
	memset(f, 0x3f, sizeof(f)), f[0] = 0;
	ans = 0x3f3f3f3f3f3f3f3f;
	for(register int i = 1; i <= n; ++i) {
		mn = 0x3f3f3f3f3f3f3f3f;
		for(register int j = 0; j <= n; ++j) {
			mn = min(mn, f[j]);
			if(pos[i] < j) f[j] = mn + A;
			else if(pos[i] > j) f[j] = mn + B;
			else f[j] = mn;
		}
	}
	for(register int i = 1; i <= n; ++i)
		ans = min(f[i], ans);
	printf("%lld", ans);
	return 0;
} 
```