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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

import sys
from collections import defaultdict

sys.setrecursionlimit(4000)

n = int(input())
arr = map(int, input().split())
arr = tuple(sorted(enumerate(arr), key=lambda tpl: -tpl[1]))

dp = defaultdict(int)

for ln in range(n + 1):
  for rn in range(n + 1 - ln):
    if ln + rn > n or dp[ln, rn]:
      continue

    p, a = arr[ln + rn - 1]
    val_l = dp[ln - 1, rn] + a * abs(p - (ln - 1)) if ln > 0 else 0
    val_r = dp[ln, rn - 1] + a * abs(p - (n - rn)) if rn > 0 else 0

    dp[ln, rn] = max(val_l, val_r)

print(max([dp[i, n - i] for i in range(n + 1)]))