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()))
l = [[0,0]]
t = [0]
p = 0
m = max(a)
z = [0,n-1]
for i in range(n):
    p += a[i]
    l.append([p,0])
    if(t[-1] < a[i]):
        t.append(a[i])
    else:
        for j in range(len(t)):
            if(t[j] >= a[i]):
                if(t[j] > a[i]):
                    t.insert(j,a[i])
                break
for i in range(n):
    l[i][1] = p-l[i+1][0]
p = 0
for i in range(1,len(t)):
    temp = [x for x, val in enumerate(a) if val == t[-i]]
    for j in range(len(temp)):
        q = l[temp[j]] 
        if(q[0] > q[1]):
            for k in range(temp[j]):
                l[k][0] -= a[temp[j]]
            p += abs(temp[j]-z[0])*a[temp[j]]
            z[0] += 1
        else:
            for k in range(temp[j]+1,n):
                l[k][1] -= a[temp[j]]
            p += abs(temp[j]-z[1])*a[temp[j]]
            z[1] -= 1
print(p)