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)

import copy
n = int(input())
a = list(map(int, input().split()))
array = [(a[i], i+1) for i in range(n)]
array.sort(reverse=True)
dp = [[0 for i in range(n+1)] for j in range(n+1)]
for i in range(n):
    for j in range(n):
        if i + j >= n:
            break
        count = i + j
        #右に移した場合
        value, index = array[count]
        dp[i][j+1] = max(dp[i][j+1], dp[i][j] + value * abs((n - j) - index))
        dp[i+1][j] = max(dp[i+1][j], dp[i][j] + value * abs((i + 1) - index))
ans = 0
for i in range(n+1):
    for j in range(n+1):
        ans = max(ans, dp[i][j])
print(ans)