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-----
4
1 3 4 2

-----Sample Output-----
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.

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