#include <bits/stdc++.h>
#define inf (long long)(1e18)
using namespace std;

long long n, a, b;
vector<int> p;
vector<vector<long long>> dp;

long long solve();

int main() {
  cin >> n >> a >> b;
  p.resize(n);
  for (auto &x : p) cin >> x;
  cout << solve() << endl;
  return 0;
}

long long solve() {
  long long res = inf;
  dp.assign(n + 1, vector<long long>(n + 1, inf));
  dp[0][0] = 0;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j <= n; ++j)
      if (p[i] < j)
        dp[i + 1][j] = dp[i][j] + b;
      else if (p[i] > j)
        dp[i + 1][j] = dp[i][j] + a;
      else
        for (int k = 0; k < j; ++k) dp[i + 1][j] = min(dp[i + 1][j], dp[i][k]);
  for (int i = 0; i <= n; ++i) res = min(res, dp[n][i]);
  return res;
}
### 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>
#define inf (long long)(1e18)
using namespace std;

long long n, a, b;
vector<int> p;
vector<vector<long long>> dp;

long long solve();

int main() {
  cin >> n >> a >> b;
  p.resize(n);
  for (auto &x : p) cin >> x;
  cout << solve() << endl;
  return 0;
}

long long solve() {
  long long res = inf;
  dp.assign(n + 1, vector<long long>(n + 1, inf));
  dp[0][0] = 0;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j <= n; ++j)
      if (p[i] < j)
        dp[i + 1][j] = dp[i][j] + b;
      else if (p[i] > j)
        dp[i + 1][j] = dp[i][j] + a;
      else
        for (int k = 0; k < j; ++k) dp[i + 1][j] = min(dp[i + 1][j], dp[i][k]);
  for (int i = 0; i <= n; ++i) res = min(res, dp[n][i]);
  return res;
}
```