Square Stamping

문제

In the plane, there are $nn$ points whose $yy$-coordinates are either $-9999-9999$, $00$, or $99999999$. Let $PP$ be the set of these $nn$ points. Your task is to enclose all the points in $PP$ by a minimum number of congruent axis-parallel squares of side length $1000010\backslash ,000$. As a subset of the plane, each such square consists of all points inside and on the boundary.

입력

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

출력

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 $tt$ such that there exist $tt$ axis-parallel squares of side length $1000010\backslash ,000$ whose union encloses all the input points in $PP$.