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: Accepted)

n=int(input())
a=list(map(int,input().split()))
li = list(enumerate(a))
li.sort(key = lambda x:x[1])
li.reverse()

dp = [[0 for _ in range(n+1)]for __ in range(n+1)]
ans = 0
for i in range(n+1):
    for j in range(n+1):
        cnt = i + j
        if cnt == 0: continue
        if cnt > n: continue
        if i == 0:
            dp[0][j] = dp[0][j-1] + li[cnt-1][1] * ((n - j) - li[cnt-1][0])
            continue
        if j == 0:
            dp[i][0] = dp[i-1][0] + li[cnt-1][1] * (li[cnt-1][0] - (i-1) )
            continue
        
        
        res1 = dp[i][j-1] + li[cnt-1][1] * (n - j - li[cnt-1][0])
        res2 = dp[i-1][j] + li[cnt-1][1] * (li[cnt-1][0] - (i-1))
        dp[i][j] = max(res1,res2)
        if cnt ==n:
            ans = max(ans,dp[i][j])

print(ans)