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: Time Limit Exceeded)

import sys 
import numpy as np
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
N = int(readline())
A = list(map(int,readline().split()))
A_sort = list(np.sort(A)[::-1])
A_index = list(np.argsort(A)[::-1])

dp = [-float('inf')]*(N+1)
dp[0] = 0

for i in range(N):
    dp_new = [-float('inf')]*(N+1)
    pi = A_index[i]  #もともといた場所
    for l in range(i+1): 
        r = i - l   #右を選んだ回数
        dp_new[l+1] = max(dp_new[l+1],dp[l] + A_sort[i] * (pi-l)) 
        dp_new[l] = max(dp_new[l],dp[l] + A_sort[i] * ((N-r-1)-pi))
    dp = dp_new
print(max(dp))