#include "bits/stdc++.h"
using namespace std;
typedef long long li;

const li mod = 1e9 + 7;

int main() {
    li n, a, b;
    cin >> n >> a >> b;
    vector<li> ps(n);
    for (int i = 0; i < n; ++i) {
        cin >> ps[i];
        ps[i]--;
    }

    vector<li> costs(n, 1LL << 60);
    for (int i = 0; i < n; ++i) {
        const li x = ps[i];
        costs[x] = a * i;
        for (int j = 0; j < i; ++j) {
            if (ps[j] < x) {
                costs[x] = min(costs[x], costs[ps[j]]);
                costs[ps[j]] += a;
            } else {
                costs[ps[j]] += b;
            }
        }
    }
    const li ans = *min_element(costs.begin(), costs.end());
    cout << ans << endl;
    
    return 0;
}

### 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
#include "bits/stdc++.h"
using namespace std;
typedef long long li;

const li mod = 1e9 + 7;

int main() {
    li n, a, b;
    cin >> n >> a >> b;
    vector<li> ps(n);
    for (int i = 0; i < n; ++i) {
        cin >> ps[i];
        ps[i]--;
    }

    vector<li> costs(n, 1LL << 60);
    for (int i = 0; i < n; ++i) {
        const li x = ps[i];
        costs[x] = a * i;
        for (int j = 0; j < i; ++j) {
            if (ps[j] < x) {
                costs[x] = min(costs[x], costs[ps[j]]);
                costs[ps[j]] += a;
            } else {
                costs[ps[j]] += b;
            }
        }
    }
    const li ans = *min_element(costs.begin(), costs.end());
    cout << ans << endl;
    
    return 0;
}

```