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 std::collections::BinaryHeap;
use std::cmp;
use num::abs;
use proconio::input;

fn main() {
    input! {
        n : usize,
        a : [i64; n]
    };
    let mut qu = BinaryHeap::new();
    for i in 0..n {
        qu.push((a[i], i));
    }
    let mut dp = vec!(vec!(0; n+1); n+1);
    for i in 0..n {
        let (v, b) = qu.pop().unwrap();
        for j in 0..n {
            if j + n - i > n {
                break;
            }
            dp[j][j+n-i-1] = cmp::max(dp[j][j+n-i-1], dp[j][j+n-i] + v * abs((j+n-i-1) as i64 - b as i64));
            dp[j+1][j+n-i] = cmp::max(dp[j+1][j+n-i], dp[j][j+n-i] + v * abs(j as i64 - b as i64));
        }
    }
    let mut res = 0;
    for i in 0..=n {
        res = cmp::max(res, dp[i][i]);
    }
    println!("{}", res);
}