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: Wrong Answer)



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

public class Main {
    static class Solution {

        Long[][]dp;
        public void find(int[][] arr, int n) {
            dp = new Long[n+2][n+2];
            Arrays.sort(arr, (a,b) -> b[0] - a[0]);
            long res = findMax(arr, 0, n-1, 0);
            System.out.println(res);
        }

        long findMax(int[][] arr, int l, int r, int index) {

            if(l>r) return 0;
            if(index >= arr.length) return 0;
            if(dp[l][r] != null) return dp[l][r];
            long ans = arr[index][0] * Math.abs(arr[index][1] - l) + findMax(arr, l+1, r, index+1);
            long ans2 = arr[index][0] * Math.abs(arr[index][1] - r) + findMax(arr, l, r-1, index+1);
            return dp[l][r] = Math.max(ans, ans2);
        }
    }

    public static void main(String[] args) {
        Solution sol = new Solution();
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[][] arr = new int[n+1][2];
        for(int i=0; i<n; i++) {
            arr[i][0] = sc.nextInt();
            arr[i][1] = i;
        }
        sol.find(arr, n);
    }
}