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 PyPy3 (7.3.0) (judge verdict: Accepted)

from bisect import bisect_left
N = int(input())
As = [(x, i) for i, x in enumerate(map(int, input().split()))]

up = sorted(As)
dp = [[0]*(N+1) for _ in range(N+1)]

for i, (u, idx) in enumerate(up[::-1], 1):
    for j in range(i):
        left = j
        right = N-(i-j)
        dp[i][j] = max(dp[i][j], dp[i-1][j]+u*abs(right-idx))
        dp[i][j+1] = max(dp[i][j+1], dp[i-1][j]+u*abs(left-idx))

print(max(dp[-1]))