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: Wrong Answer)

use std::io;
use std::str::FromStr;
use std::collections::HashSet;

fn input<T:FromStr>() -> T {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.trim().parse().ok().unwrap()
}

fn input_vec() -> Vec<u64> {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.split_whitespace().map(|s| s.parse().unwrap()).collect()
}

fn main() {
    let n: usize = input();
    let mut a_vec = input_vec();
    let mut left = 0usize;
    let mut right = n - 1;
    let mut deleted: HashSet<usize> = HashSet::new();

    let mut sum = 0;
    for _ in 0..n {  
        let mut max = 0;
        let mut max_idx = 0usize;      
        let mut is_left = false;
        for i in 0..a_vec.len() {
            if deleted.contains(&i) {
                continue;
            }
            let happiness: u64;
            let mut is_left_buf = false;
            
            let happiness_left: u64;
            let happiness_right: u64;
            if i < left {
                happiness_left = a_vec[i] * (left - i) as u64;
            } else {
                happiness_left = a_vec[i] * (i - left) as u64;
            }
            if i < right {
                happiness_right = a_vec[i] * (right - i) as u64;
            } else {
                happiness_right = a_vec[i] * (i - right) as u64;
            }

            if happiness_left < happiness_right {
                happiness = happiness_right;                
            } else {
                happiness = happiness_left;
                is_left_buf = true;
            }

            if happiness > max {
                max = happiness;
                max_idx = i;
                is_left = is_left_buf;
            }
        }
        sum += max;
        deleted.insert(max_idx);
        if is_left {
            left += 1;
        } else {
            right -= 1;
        }
        // println!("happiness = {}, idx = {}, left = {}, right = {}", max, max_idx, left, right);
    }
    
    println!("{}", sum);
}