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.

Examples

Input

4
1 3 4 2

Output

20

Input

6
5 5 6 1 1 1

Output

58

Input

6
8 6 9 1 2 1

Output

85

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