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)

#設定
import sys
input = sys.stdin.buffer.readline

#ライブラリインポート
from collections import defaultdict

con = 10 ** 9 + 7
#入力受け取り
def getlist():
	return list(map(int, input().split()))

#処理内容
def main():
	N = int(input())
	A = getlist()
	S = []
	for i in range(N):
		for j in range(N):
			S.append([A[i] * abs(i - j), -A[i], i, j])

	S = sorted(S)
	Ajudi = [0] * N
	Ajudj = [0] * N
	Lis = [0] * N
	ans = 0
	# print(S)
	for i in range(N ** 2):
		cur = N ** 2 - 1 - i
		if Ajudi[S[cur][2]] == 0 and Ajudj[S[cur][3]] == 0:
			Ajudi[S[cur][2]] = 1
			Ajudj[S[cur][3]] = 1
			Lis[S[cur][3]] = S[cur][0]
			ans += S[cur][0]

	# print(Lis)
	print(ans)

if __name__ == '__main__':
	main()