p03092 AtCoder Grand Contest 032 - Rotation Sort
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
```python
import sys
readline = sys.stdin.readline

N, A, B = map(int, readline().split())
*P, = map(int, readline().split())
Q = [0]*N
for i, p in enumerate(P):
    Q[p-1] = i

INF = 10**18
dp = [[INF]*(N+1) for i in range(N+1)]
dp[0][0] = 0
for i in range(N):
    qi = Q[i]
    for j in range(N):
        v = dp[i][j]
        dp[i+1][j] = min(dp[i+1][j], v + (A if qi < j else B))
        dp[i][j+1] = min(dp[i][j+1], v)
        if Q[i] == j:
            dp[i+1][j+1] = min(dp[i+1][j+1], v)
for i in range(N):
    dp[i+1][N] = min(dp[i+1][N], dp[i][N] + A)
for j in range(N):
    dp[N][j+1] = min(dp[N][j+1], dp[N][j])
sys.stdout.write("%d\n" % dp[N][N])
```