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.io.*;
import java.math.BigInteger;
import java.util.*;

 class Main {

	static long sx = 0, sy = 0, mod = (long) (1e9 + 7);

	static ArrayList<Integer>[] a;
	static long[][] dp;
	static long[] fa;
	static long[] farr;
	public static PrintWriter out;
	static ArrayList<pair> pa = new ArrayList<>();
	static long[] fact = new long[(int) 1e6];
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long m = 998244353;
	static long[] no, col;
	// static String s;
	static long k = 0, n = 0;
	static int[] c;
	static long ans = 0;
	static int[] down;
	static int[] score;
	static HashSet<Integer> hm = new HashSet<>();

	public static void main(String[] args) throws IOException {

		// Scanner scn = new Scanner(new BufferedReader(new
		// InputStreamReader(System.in)));

		out = new PrintWriter(System.out);
		Reader scn = new Reader();

		int n = scn.nextInt();

		ArrayList<pair> p = new ArrayList<>();

		for (int i = 1; i <= n; i++)
			p.add(new pair(i, scn.nextLong()));

		Collections.sort(p);

		dp = new long[n+5][n+5];
		
		for(int i=0; i<dp.length; i++)
			 Arrays.fill(dp[i], -1);
		
		long ans = f(p, 0, 1);
		
		
		

		System.out.println(ans);

	}

	private static long f(ArrayList<pair> p, int i, int l) {

		int r = p.size() - (i - (l - 1));

		if (i == p.size())
			return 0;
		
		if(dp[i][l]!=-1)
			return dp[i][l];

		int left = Math.abs(p.get(i).i - l);
		int right = Math.abs(r - p.get(i).i);

		long ans = 0;

		ans = Math.max(f(p, i + 1, l + 1) + p.get(i).val * left, f(p, i + 1, l) + p.get(i).val * right);

		return dp[i][l] = ans;
	}
	// _________________________TEMPLATE_____________________________________________________________

	// public static long lcm(long x, long y) {
	//
	// return (x * y) / gcd(x, y);
	// }
	//
	// private static long gcd(long x, long y) {
	// if (x == 0)
	// return y;
	//
	// return gcd(y % x, x);
	// }
	//
	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer p1, Integer p2) {
	//
	// return p2 - p1;
	//
	// }
	// }
	//
	// }
	//
	public static long pow(long a, long b) {

		if (b < 0)
			return 0;
		if (b == 0 || b == 1)
			return (long) Math.pow(a, b);

		if (b % 2 == 0) {

			long ret = pow(a, b / 2);
			ret = (ret % mod * ret % mod) % mod;
			return ret;
		}

		else {
			return ((pow(a, b - 1) % mod) * a % mod) % mod;
		}
	}

	private static class pair implements Comparable<pair> {

		int i;
		long val;

		pair(int a, long b) {
			i = a;
			val = b;
		}

		@Override
		public int compareTo(pair o) {

			return (int) (o.val - this.val);
		}

		// @Override
		//
		// public int hashCode() {
		// return i;
		// }
		//
		// @Override
		//
		// public boolean equals(Object o) {
		//
		// pair p = (pair) o;
		// return this.i == p.i;
		// }

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

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

		public Reader(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[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		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 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 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;
		}

		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();
		}

		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[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}

		public long[][] nextInt2DArrayL(int m, int n) throws IOException {
			long[][] arr = new long[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}