#pragma GCC optimize("trapv")
#include<bits/stdc++.h>
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define pb push_back
using namespace std;
using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
const int maxn = 5e3 + 55;
ll n, a, b, dp[maxn][maxn], p[maxn];
ll cost(int i, int j) {
	if(p[i]==j-1) return 0;
	return p[i] < j-1 ? a : b;
}
int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n >> a >> b;
	for(int t, i = 1; i <= n; i++) {
		cin >> t;
		p[t] = i;
	}
	memset(dp, 0x3f, sizeof dp);
	for(int i = 0; i <= n+1; i++)
		dp[0][i] = 0;
	for(int i = 1; i <= n; i++) {
		for(int j = 1; j <= n+1; j++) {
			dp[i][j] = min(dp[i][j-1], dp[i-1][j] + cost(i, j));
		}
	}
	cout << dp[n][n+1];
}

### Prompt

In CPP, your task is to solve 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
#pragma GCC optimize("trapv")
#include<bits/stdc++.h>
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define pb push_back
using namespace std;
using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
const int maxn = 5e3 + 55;
ll n, a, b, dp[maxn][maxn], p[maxn];
ll cost(int i, int j) {
	if(p[i]==j-1) return 0;
	return p[i] < j-1 ? a : b;
}
int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n >> a >> b;
	for(int t, i = 1; i <= n; i++) {
		cin >> t;
		p[t] = i;
	}
	memset(dp, 0x3f, sizeof dp);
	for(int i = 0; i <= n+1; i++)
		dp[0][i] = 0;
	for(int i = 1; i <= n; i++) {
		for(int j = 1; j <= n+1; j++) {
			dp[i][j] = min(dp[i][j-1], dp[i-1][j] + cost(i, j));
		}
	}
	cout << dp[n][n+1];
}

```