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: Wrong Answer)

import math  # noqa
import bisect  # noqa
import queue  # noqa


if __name__ == '__main__':
    N = int(input())
    A = list(map(int, input().split()))

    MAX = N - 1
    MIN = 0
    used = set()

    ans = 0
    while len(used) < N:
        diff = []
        for i, a in enumerate(A):
            res = max(abs(i - MIN), abs(MAX - i))
            if i not in used:
                diff.append([res * a, i])
        diff.sort(reverse=True)
        ans += diff[0][0]
        used.add(diff[0][1])
        idx = 0
        while abs(diff[idx][1] - MIN) == abs(MAX - diff[idx][1]):
            idx += 1
            if idx == len(diff):
                idx -= 1
                break
        if abs(diff[idx][1] - MIN) < abs(MAX - diff[idx][1]):
            MAX -= 1
        else:
            MIN += 1

    print(ans)