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: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.DataInputStream;
import java.util.HashMap;
import java.io.IOException;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.util.Map;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author iavanish
 */
public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EActiveInfants solver = new EActiveInfants();
        solver.solve(1, in, out);
        out.close();
    }

    static class EActiveInfants {

        private Map<Integer, Map<String, Long>> mem;

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextLong();
            }

            long[][] dp = new long[n][n];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i != j) {
                        dp[i][j] = a[i] * Math.abs(i - j);
                    }
                }
            }

            mem = new HashMap<>();
            StringBuilder chosen = new StringBuilder();
            for (int i = 0; i < n; i++) {
                mem.put(i, new HashMap<>());
                chosen.append('0');
            }
            out.println(maximize(dp, chosen, n, 0));
        }

        private long maximize(long[][] dp, StringBuilder chosen, int n, int currI) {
            if (currI == n) {
                return 0;
            }
            if (mem.containsKey(currI) && mem.get(currI).containsKey(chosen.toString())) {
                return mem.get(currI).get(chosen.toString());
            }
            long max = 0;
            for (int i = 0; i < n; i++) {
                if (chosen.charAt(i) == '0') {
                    chosen.setCharAt(i, '1');
                    max = Math.max(max, dp[currI][i] + maximize(dp, chosen, n, currI + 1));
                    chosen.setCharAt(i, '0');
                }
            }
            mem.get(currI).put(chosen.toString(), max);
            return max;
        }

    }

    static class FastReader {

        private final int BUFFER_SIZE = 1 << 16;
        private final InputStream inputStream;
        private final byte[] buffer;
        private int bufferPointer;
        private int bytesRead;

        public FastReader() {
            this.inputStream = new DataInputStream(System.in);
            this.buffer = new byte[BUFFER_SIZE];
            this.bufferPointer = bytesRead = 0;
        }

        public FastReader(InputStream inputStream) {
            this.inputStream = inputStream;
            this.buffer = new byte[BUFFER_SIZE];
            this.bufferPointer = bytesRead = 0;
        }

        public FastReader(String fileName) {
            try {
                this.inputStream = new DataInputStream(new FileInputStream(fileName));
                this.buffer = new byte[BUFFER_SIZE];
                this.bufferPointer = bytesRead = 0;
            } catch (FileNotFoundException e) {
                throw new RuntimeException(e);
            }
        }

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

        public long nextLong() {
            long nextLong = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean negative = (c == '-');
            if (negative) {
                c = read();
            }
            do {
                nextLong = nextLong * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (negative) {
                return -nextLong;
            }
            return nextLong;
        }

        private void fillBuffer() {
            try {
                bytesRead = inputStream.read(buffer, bufferPointer = 0, BUFFER_SIZE);
                if (bytesRead == -1) {
                    buffer[0] = -1;
                }
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

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

    }

}