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 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;

public class Main {

    static List<int[]> list;

    static long find(int s,int l,int n,long [][] dp){
        if(s+l==n)return 0;
        if(dp[s][l]!=-1)return dp[s][l];

        int currIndex=s+l;
        int currElement=list.get(currIndex)[1];
        int elementIndex=list.get(currIndex)[0];

        long a=(long)currElement*Math.abs(elementIndex-s)+
                                 find(s+1,l,n,dp);
        long b=(long)currElement*Math.abs(n-l-1-elementIndex)+
                                 find(s,l+1,n,dp);
        
        return dp[s][l]=Math.max(a,b);
    }
    public static void main(String [] args) throws IOException{
        FastScanner sc=new FastScanner();
        int n=sc.nextInt();
        int [] a=sc.nextIntArray(n);
        //[0] ind ,[1] val
        list=new ArrayList<>();
        for(int i=0;i<n;i++)list.add(new int[]{i,a[i]});
        list.sort((aa,bb)->bb[1]-aa[1]);
        long [][] dp=new long[n+1][n+1];
        for(int i=0;i<=n;i++)Arrays.fill(dp[i],-1);
        long ans=find(0,0,n,dp);
        System.out.println(ans);


    }

}



























class FastScanner{	
    private int BUFFER_SIZE = 1 << 16;
   
   private  DataInputStream din;
   
   private  byte[] buffer;
   
   private int bufferPointer, bytesRead;
   
   public FastScanner() {
       din = new DataInputStream(System.in);
       buffer = new byte[BUFFER_SIZE];
       bufferPointer = bytesRead = 0;
   }

   public FastScanner( String file_name) throws IOException {
       din = new DataInputStream(new FileInputStream(file_name));
       buffer = new byte[BUFFER_SIZE];
       bufferPointer = bytesRead = 0;
   }
   
   public String readLine() throws IOException {
        byte[] buf = new byte[64];
       int cnt = 0, c;
       while ((c = read()) != -1) {
           if (c == '\n')
               break;
           buf[cnt++] = (byte) c;
       }
       return new String(buf, 0, cnt);
   }
   
   public String next() throws IOException{

       byte c = read();
       while(Character.isWhitespace(c)){
           c = read();
       }
       
        StringBuilder builder = new StringBuilder();
       builder.append((char)c);
       c = read();
       while(!Character.isWhitespace(c)){
           builder.append((char)c);
           c = read();
       }
       
       return builder.toString();
   }

   public int nextInt() throws IOException {
       int ret = 0;
       byte c = read();
       while (c <= ' ')
           c = read();
        boolean neg = (c == '-');
       if (neg)
           c = read();
       do {
           ret = ret * 10 + c - '0';
       } while ((c = read()) >= '0' && c <= '9');

       if (neg)
           return -ret;
       return ret;
   }
   
   public int[] nextIntArray( int n) throws IOException {
        int arr[] = new int[n];
       for(int i = 0; i < n; i++){
           arr[i] = nextInt();
       }
       return arr;
   }

   public long nextLong() throws IOException {
       long ret = 0;
       byte c = read();
       while (c <= ' ')
           c = read();
        boolean neg = (c == '-');
       if (neg)
           c = read();
       do {
           ret = ret * 10 + c - '0';
       } while ((c = read()) >= '0' && c <= '9');
       if (neg)
           return -ret;
       return ret;
   }
   
   public long[] nextLongArray( int n) throws IOException {
        long arr[] = new long[n];
       for(int i = 0; i < n; i++){
           arr[i] = nextLong();
       }
       return arr;
   }

   public char nextChar() throws IOException{
       byte c = read();
       while(Character.isWhitespace(c)){
           c = read();
       }
       return (char) c;	
   }
   
   public double nextDouble() throws IOException {
       double ret = 0, div = 1;
       byte c = read();
       while (c <= ' ')
           c = read();
        boolean neg = (c == '-');
       if (neg)
           c = read();

       do {
           ret = ret * 10 + c - '0';
       } while ((c = read()) >= '0' && c <= '9');

       if (c == '.') {
           while ((c = read()) >= '0' && c <= '9') {
               ret += (c - '0') / (div *= 10);
           }
       }

       if (neg)
           return -ret;
       return ret;
   }
   
   public double[] nextDoubleArray( int n) throws IOException {
        double arr[] = new double[n];
       for(int i = 0; i < n; i++){
           arr[i] = nextDouble();
       }
       return arr;
   }

   private void fillBuffer() throws IOException {
       bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
       if (bytesRead == -1)
           buffer[0] = -1;
   }

   private byte read() throws IOException {
       if (bufferPointer == bytesRead)
           fillBuffer();
       return buffer[bufferPointer++];
   }

   public void close() throws IOException {
       if (din == null)
           return;
       din.close();
   }

}