$f(x, y)$ return the number of places a knight can move to (in one move) on a standard $8\times8$ chess board from the given $(x, y)$ position. What is the sum of $f(x, y)$ for all $x$ and $y$?

LetHere are some explicit examples:

- $f(0, 0) = 2$, $f(5, 3) = 8$, $f(7, 7) = 2$.