For the function $f(x,y)$ below, determine whether there is a value for $c$ making the function continuous everywhere. If so, find it. $$f(x,y) = \begin{cases} c + y & x \le 2, \\ 5 - y & x > 2 \end{cases}$$

$c =$
(If there is no value of $c$ that works, enter none, and be sure that you can explain why there is no such value.)