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: Wrong Answer)

n = int(input())
a = list(map(int, input().split()))

left = 0
right = len(a) - 1
ans = 0

for i in range(n):
    # print(right, left)
    tmp = 0
    num = 0
    l, r = False, False
    for j in range(len(a)):
        if abs(j - right) > abs(j - left):
            if tmp < abs(j - right) * a[j]:
                tmp = abs(j - right) * a[j]
                num = j    
                l, r = False, True

        elif abs(j - right) < abs(j - left):
            if tmp < abs(j - left) * a[j]:
                tmp = abs(j - left) * a[j]
                num = j    
                l, r = True, False

        else:
            if tmp < abs(j - left) * a[j]:
                for k in range(len(a)):
                    tl, tr = False, False
                    te = 0
                    if k != j:
                        if abs(k - right) > abs(j - left):
                            if te < abs(k - right) * a[k]:
                                te = abs(k - right) * a[k]
                                tl, tr = False, True
                        else:
                            if te < abs(k - left) * a[k]:
                                te = abs(k - left) * a[k]
                                tl, tr = True, False
                num = j
                if tl:
                    l, r = False, True
                    tmp += abs(j - right) * a[j]
                else:
                    l, r = True, False
                    tmp += abs(j - left) * a[j]
                
    ans += tmp    
    a[num] = 0
   
    if l:
        left += 1
    if r:
        right -= 1

print(ans)