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, fastout};
use std::cmp::max;
use num::abs;


#[fastout]
fn main() {
    input! {
        n: usize,
        aaa: [usize; n],
    }

    let mut aaa_with_idx: Vec<(usize, &usize)> = aaa.iter().enumerate().collect();
    aaa_with_idx.sort_by(|a, b| { a.1.cmp(b.1) });
    aaa_with_idx.reverse();

    let ni = n as isize;

    let mut dp = vec![0];

    for k in 1..=n {
        let mut ndp = vec![0; k + 1];
        let ai = aaa_with_idx[k - 1];
        let ki = k as isize;
        let i = ai.0 as isize;
        let a = *ai.1 as isize;
        for l in 0..k {
            let li = l as isize;
            ndp[l + 1] = max(ndp[l + 1], dp[l] + a * abs(i - li));
            ndp[l] = max(ndp[l], dp[l] + a * abs(ni - ki + li - i));
        }
        dp = ndp;
    }

    let ans = dp.iter().max().unwrap();

    println!("{:?}", ans);
}