Score : $500$ points
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 is given from Standard Input in the following format:
$N$ $A_1$ $A_2$ $...$ $A_N$
Print the maximum total happiness points the children can earn.
4 1 3 4 2
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.
6 5 5 6 1 1 1
58
6 8 6 9 1 2 1
85