Alter Ego

Consider an array $A$ of size $N$: $A_1, A_2, \ldots, A_N$, where $N$ is even. The $AlterEgo$ of this array $A$, is another array $B$, which is computed as follows: 1. Start with an empty array $B$. 2. For $i$ ranging from $1$ to $\frac{N}{2}$, insert the elements $(A_i + A_{i+\frac{N}{2}})$ and $|A_i - A_{i+\frac{N}{2}}|$ to the end of array $B$. Here $|x|$ refers to absolute value of $x$. 3. Re