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.

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.

Constraints

• $2 \leq N \leq 2000$
• $1 \leq A_i \leq 10^9$
• All values in input are integers.

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

见题面 Input 部分

见题面 Output 部分