Christmas frenzy

Christmas is a popular festival in Turing Land. Turing Land can be thought of as a 2D plane. The point $(a,b)$ denotes that the $x$ coordinate of the point is $a$ and the $y$ coordinate is $b$. The road network in Turing Land is in such a way that, from a point $(a,b)$, there is road connecting each of $(a+1,b)$,$(a-1,b)$,$(a,b+1)$,$(a,b-1)$, each of which are at a distance of $1$ unit from $(a