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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = Integer.parseInt(scan.next());

        AObj[] a = new AObj[n];
        for (int i = 0; i < n; i++) {
            a[i] = new AObj(i, Integer.parseInt(scan.next()));
        }
        scan.close();

        Arrays.sort(a, (x, y) -> y.value_ - x.value_);

        long[][] dp = new long[n + 1][n + 1];
        dp[0][0] = 0;

        for (int i = 0; i < n; i++) {
            for (int x = 0; x <= i; x++) {
                int y = i - x;
                dp[x + 1][y] = Math.max(dp[x + 1][y], dp[x][y] + (long)Math.abs(x - a[i].index_) * a[i].value_);
                dp[x][y + 1] = Math.max(dp[x][y + 1], dp[x][y] + (long)Math.abs(a.length - 1 - y - a[i].index_) * a[i].value_);
            }
        }

        long sum = 0;
        for (int i = 0; i < n; i++) {
            if (sum < dp[i][n - i]) {
                sum = dp[i][n - i];
            }
        }
        System.out.println(sum);
    }

}

class AObj {
    int index_;
    int value_;

    public AObj(int index, int value) {
        index_ = index;
        value_ = value;
    }
}