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: Runtime Error)

N = int(input())
A = list(map(int, input().split()))

a = [(i, ai) for i, ai in enumerate(A)]
a = sorted(key=lambda x: x[1], reverse=True)

# import numpy as np
# dp = np.zeros((N+1, N+1), np.int8)

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

dp[0][0] = 0
for i, ai in enumerate(a):
    for l in range(i+1):
        r = i - l
        dp[i+1][l] = max(dp[i+1][l], dp[i][l] + ai[1] * ((N-1-r) - ai[0]))
        dp[i+1][l+1] = max(dp[i+1][l+1], dp[i][l] + ai[1] * (ai[0] - l))

print(max(dp[N]))