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: Wrong Answer)

import heapq
from collections import defaultdict, deque
from math import ceil, factorial, gcd
from itertools import accumulate
import sys
import bisect

sys.setrecursionlimit(10 ** 7)
INF = float("inf")
MOD = 10 ** 9 + 7

si = lambda: input().strip()
ii = lambda: int(input())
mii = lambda: map(int, input().split())
lmii = lambda: list(map(int, input().split()))
smii = lambda: sorted(map(int, input().split()))

# ----------

N = ii()
A = lmii()

scoret = set()

for i in range(N):
    for j in range(N):
        scoret.add((i, j, A[i] * abs(i-j)))

scoret = list(scoret)
scoret.sort(key=lambda x: -x[2])
done_s = set()
done_t = set()
ans = 0
cnt = 0
for s, t, score in scoret:
    if cnt == N:
        break
    if s in done_s or t in done_t:
        continue
    ans += score
    done_s.add(s)
    done_t.add(t)
    cnt += 1

print(ans)