Nearest Court

Chef and Chefina are at positions $X$ and $Y$ on a number line. They both love badminton. It is known that badminton courts are located at every integer point. They want to find a court such that the *maximum* distance travelled by either of them is **minimized**. Formally, suppose they choose the badminton court at position $Z$. You need to find the minimum value of $\max(|X-Z|, |Y-Z|)$ acros