Square Stamping

In the plane, there are $n$ points whose $y$-coordinates are each one of $-9999$, $0$, or $9999$. Let $P$ be the set of these $n$ points. Your task is to enclose all points in $P$ with a minimum number of congruent axis-parallel squares of side length $10000$. Each square is a closed region, so it contains all points inside it and on its boundary.

The first line contains an integer $n$ ($1 \le n \le 300000$), the number of points in $P$. Each of the following $n$ lines contains two integers $x$ and $y$, the coordinates of a point. Here $-10^9 \le x \le 10^9$ and $y \in \{-9999, 0, 9999\}$. All input points are distinct.

Print one line containing the minimum number $t$ such that $t$ axis-parallel squares of side length $10000$ have a union that encloses all points in $P$.