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: Time Limit Exceeded)

from operator import itemgetter
import sys
sys.setrecursionlimit(10**5)

def f(x, po, h, t, ple):
    if po=='h':
        ple+=B[x][1]*abs(B[x][0]-h)
        h+=1
    else:
        ple+=B[x][1]*abs(B[x][0]-t)
        t-=1
    if h>t:
        return ple
    
    ans1=f(x+1, 'h', h, t, ple)
    ans2=f(x+1, 't', h, t, ple)
    return max(ans1, ans2)

N=int(input())
A=list(map(int, input().split()))
B=[[i, A[i]] for i in range(N)]
B=sorted(B, key=itemgetter(1), reverse=True)
h=0
t=N-1
ans1=f(0, 'h', h, t, 0)
ans2=f(0, 't', h, t, 0)
print(max(ans1, ans2))