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: Runtime Error)

n = int(input())
li = list(map(int,input().split()))
import copy

def maxmize(members, seats):
    if seats == []:
        return 0
    else:
        saidai = max(members)
        saidai_index = members.index(saidai)
        newmembers = copy.deepcopy(members)
        newmembers[saidai_index] = 0
        #print("members",members)
        #print("seats",seats[:-1])
        #print("saidai",saidai)
        #print("hoge",abs(saidai_index - seats[-1]))
        right = maxmize(newmembers,seats[:-1]) + saidai * abs(saidai_index - seats[-1])
        left = maxmize(newmembers,seats[1:]) + saidai * abs(saidai_index - seats[0])                                                      
        
        #print(left,right)
    return max(left,right)

givenseats = [j for j in range(n)]
maxmize(li, givenseats)