HMMT November 2016 U22

Let the function $f: \mathbb{Z} \rightarrow \mathbb{Z}$ take only integer inputs and have integer outputs. For any integers $x$ and $y, f$ satisfies

$$f(x)+f(y)=f(x+1)+f(y-1)$$

If $f(2016)=6102$ and $f(6102)=2016$, what is $f(1) ?$