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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
$N = (int)trim(fgets(STDIN));
$A = explode(' ', fgets(STDIN));
$A = array_map(function ($a) {
    return (int)$a;
}, $A);
$ans = 0;
$prefix = 0;
$suffix = 0;

while ($prefix + $suffix < $N) {
    $max = 0;
    $to_front = false;
    $max_i = 0;
    for ($i = 0; $i < $N; $i++) {
        if ($i < ($N - $suffix) / 2) {
            $new_happy = $A[$i] * ($N - $i - 1 - $suffix);
            if ($new_happy > $max || ($new_happy === $max && $A[$i] > $A[$max_i])) {
                $max = $new_happy;
                $to_front = false;
                $max_i = $i;
            }
        } else {
            $new_happy = $A[$i] * ($i - $prefix);
            if ($new_happy > $max || ($new_happy === $max && $A[$i] > $A[$max_i])) {
                $max = $new_happy;
                $to_front = true;
                $max_i = $i;
            }
        }
    }
    if ($to_front) {
        $prefix += 1;
    } else {
        $suffix += 1;
    }
    $A[$max_i] = 0;
    $ans += $max;
    $max = 0;
}

echo $ans;