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: Accepted)

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

for ($i = 0; $i < $N; $i++) {
    $max_A = max($A);
    $index = array_keys($A, $max_A)[0];
    $A[$index] = 0;
    $dp[$i + 1][0] = $dp[$i][0] + $max_A * abs($N - ($i + 1) - $index);
    for ($l = 0; $l < $i; $l++) {
        $dp[$i + 1][$l + 1] = max($dp[$i][$l + 1] + $max_A * abs(($N - ($i - $l)) - $index), $dp[$i][$l] + $max_A * abs($index - $l));
    }
    $dp[$i + 1][$i + 1] = $dp[$i][$i] + $max_A * abs($index - $i);
}

for ($i = 0; $i <= $N; $i++) {
    $ans = max($dp[$N][$i], $ans);
}

echo $ans;