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.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		Person[] persons = new Person[n];
		for (int i = 0; i < n; i++) {
		    persons[i] = new Person(i, sc.nextInt());
		}
		Arrays.sort(persons);
		long[][] dp = new long[n + 1][n + 1];
		for (int i = 1; i <= n; i++) {
		    for (int j = 0; j <= i; j++) {
		        if (j != 0) {
		            dp[j][i - j] = Math.max(dp[j][i - j], dp[j - 1][i - j] + Math.abs(j - 1 - persons[i - 1].idx) * (long)persons[i - 1].value);
		        }
		        if (j != i) {
		            dp[j][i - j] = Math.max(dp[j][i - j], dp[j][i - j - 1] + Math.abs(n - (i - j) - persons[i - 1].idx) * (long)persons[i - 1].value);
		        }
		    }
		}
		long max = 0;
		for (int i = 0; i <= n; i++) {
		    max = Math.max(max, dp[i][n - i]);
		}
		System.out.println(max);
   }
   
   static class Person implements Comparable<Person>{
       int idx;
       int value;
       
       public Person(int idx, int value) {
           this.idx = idx;
           this.value = value;
       }
       
       public int compareTo(Person another) {
           return another.value - value;
       }
   }
}