Problem:
Score : 500 points

Problem Statement

There are N children standing in a line from left to right. The activeness of the i-th child from the left is A_i.

You can rearrange these children just one time in any order you like.

When a child who originally occupies the x-th position from the left in the line moves to the y-th position from the left, that child earns A_x \times |x-y| happiness points.

Find the maximum total happiness points the children can earn.

Constraints

2 \leq N \leq 2000

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum total happiness points the children can earn.

Sample Input 1

4
1 3 4 2

Sample Output 1

20

If we move the 1-st child from the left to the 3-rd position from the left, the 2-nd child to the 4-th position, the 3-rd child to the 1-st position, and the 4-th child to the 2-nd position, the children earns 1 \times |1-3|+3 \times |2-4|+4 \times |3-1|+2 \times |4-2|=20 happiness points in total.

Sample Input 2

6
5 5 6 1 1 1

Sample Output 2

58

Sample Input 3

6
8 6 9 1 2 1

Sample Output 3

85

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
    input! {
        n: usize,
        a: [u64; n],
    }

    let mut a: Vec<(u64, usize)> = a.iter().copied().enumerate().map(|(i, x)| (x, i)).collect();
    a.sort();
    a.reverse();
    let a = a;

    let mut solve = Solve {
        n,
        a,
        memo: vec![vec![None; n + 1]; n + 1],
    };
    solve.solve();
}

struct Solve {
    n: usize,
    a: Vec<(u64, usize)>,
    memo: Vec<Vec<Option<u64>>>,
}

impl Solve {
    fn solve(&mut self) {
        let ans = self.calc(0, self.n);
        // dbg!(&self.memo);
        println!("{}", ans);
    }

    // 範囲とかをもらって、嬉しさの最大値を返す
    fn calc(&mut self, left: usize, right: usize) -> u64 {
        let n = self.n;
        let a = &self.a;

        if let Some(joy) = self.memo[left][right] {
            return joy
        }

        if left == right {
            self.memo[left][right] = Some(0);
            return 0
        }

        let next = left + (n - right);
        let (activeness, origin_i) = a[next];
        // dbg!(left, right, activeness);
        // dbg!(left, right);

        // 左に付け足す
        let ret1 = self.calc(left + 1, right) + activeness * (origin_i as i64 - left as i64).abs() as u64;
        let ret2 = self.calc(left, right - 1) + activeness * (origin_i as i64 - (right - 1) as i64).abs() as u64;
        // dbg!(activeness * (origin_i as i64 - (left + 1) as i64).abs() as u64);
        // dbg!(activeness * (origin_i as i64 - (right - 1) as i64).abs() as u64);

        let ret = std::cmp::max(ret1, ret2);
        self.memo[left][right] = Some(ret);

        // dbg!(ret);
        ret
    }
}