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: Time Limit Exceeded)

import sys

# 整数を一つ入力
N = int(input())
# スペース区切りの整数をリストに入力
t = [int(x) for x in input().split()]

A = []
for i in range(N):
    A.append([t[i],i])

#二次元配列初期化
ar = [[-1 for i2 in range(N)] for i1 in range(N)]

A.sort(reverse=True)

r_max = 0

sys.setrecursionlimit(2500)
def test(i,r,h,l,nn):
    global r_max
    if ar[h][l] > r:
        return
    else:
        ar[h][l] = r
    if i == nn:
        r_max = max(r_max, r+abs(A[i][1]-h)*A[i][0])
    else:
        if abs(h-A[i][1]) > abs(l-A[i][1]):
            test(i+1,r+abs(A[i][1]-h)*A[i][0],h-1,l,nn)
            test(i+1,r+abs(A[i][1]-l)*A[i][0],h,l+1,nn)
        else:
            test(i+1,r+abs(A[i][1]-l)*A[i][0],h,l+1,nn)
            test(i+1,r+abs(A[i][1]-h)*A[i][0],h-1,l,nn)

for n in range(5,N,2):
    test(0,0,N-1,0,n)

test(0,0,N-1,0,N-1)

print(r_max)