Square Stamping

In the plane, there are $n$ points whose $y$-coordinates are either $-9999$, $0$, or $9999$. Let $P$ be the set of these $n$ points. Your task is to enclose all the points in $P$ by a minimum number of congruent axis-parallel squares of side length $10\\,000$. As a subset of the plane, each such square consists of all points inside and on the boundary.

Your program is to read from standard input. The input starts with a line consisting of a single integer $n$ ($1 ≤ n ≤ 300\\,000$), representing the number of input points in $P$. In each of the following $n$ lines, there are two integers $x$ and $y$, representing the $x$- and $y$-coordinates of a point in $P$, respectively, such that it holds that $-10^9 ≤ x ≤ 10^9$ and $y \in \\{-9999, 0, 9999\\}$. You may assume that all the $n$ input points are distinct.

Your program is to write to standard output. Print exactly one line. The line should consist of a single integer that represents the minimum possible number $t$ such that there exist $t$ axis-parallel squares of side length $10\\,000$ whose union encloses all the input points in $P$.