Maximum Alternating Sum

The *alternating sum* of an array $A$ of length $N$ is defined to be $$ \sum_{i=1}^N (-1)^{i+1} A_i $$ If you expand it out, this is the expression $A_1 - A_2 + A_3 - A_4 + \ldots + (-1)^{N+1} A_N$. You're given an array $A$ containing $N$ integers. You can rearrange this array however you like. Find the **maximum** possible value of the alternating sum of $A$ after rearrangement. ### Input -