Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that $$f(f(x) - y) = f(x) + f(f(y) - f(-x)) + x$$for all real numbers $x$ and $y.$
Let $n$ be the number of possible values of $f(3),$ and let $s$ be the sum of all possible values of $f(3).$ Find $n \times s.$
I tried plugging in some different values of $x$ and $y$ into the functional equation, but they didn't get me anywhere. I'm not really sure what to do, and any help would be greatly appreciated!
Thanks in advance!!!