Problem:
Score : 1000 points

Problem Statement

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.

Sample Input 1

3 20 30
3 1 2

Sample Output 1

20

Shifting (p_1, p_2, p_3) to the left by one results in p = (1, 2, 3).

Sample Input 2

4 20 30
4 2 3 1

Sample Output 2

50

One possible sequence of operations is as follows:

Shift (p_1, p_2, p_3, p_4) to the left by one. Now we have p = (2, 3, 1, 4).

Shift (p_1, p_2, p_3) to the right by one. Now we have p = (1, 2, 3, 4).

Here, the total cost is 20 + 30 = 50.

Sample Input 3

1 10 10
1

Sample Output 3

0

Sample Input 4

4 1000000000 1000000000
4 3 2 1

Sample Output 4

3000000000

Sample Input 5

9 40 50
5 3 4 7 6 1 2 9 8

Sample Output 5

220

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn calc(
    depth: usize,
    v: usize,
    seq: &Vec<usize>,
    costs: &Vec<i64>,
    memo: &mut Vec<Vec<i64>>,
) -> i64 {
    let n = seq.len();
    if depth == n {
        return 0;
    }
    if memo[depth][v] != -1 {
        return memo[depth][v];
    }
    let mut ret = 1 << 60;
    if seq[depth] < v {
        // left move
        ret = std::cmp::min(ret, calc(depth + 1, v, seq, costs, memo) + costs[0]);
    } else {
        // right move
        ret = std::cmp::min(ret, calc(depth + 1, v, seq, costs, memo) + costs[1]);
        // nop
        ret = std::cmp::min(ret, calc(depth + 1, seq[depth], seq, costs, memo));
    };
    // println!("{} {} {}", depth, v, ret);
    memo[depth][v] = ret;
    return ret;
}

fn main() {
    let n = read::<usize>();
    let mut costs = vec![0, 0];
    costs[1] = read::<i64>();
    costs[0] = read::<i64>();
    let mut seq = vec![0; n];
    for i in 0..n {
        seq[i] = read::<usize>() - 1;
    }
    let mut memo = vec![vec![-1; n]; n];
    let ans = calc(0, 0, &seq, &costs, &mut memo);
    println!("{}", ans);
}