[USACO16FEB]负载平衡Load Balancing_Silver


Farmer John's $N$ cows are each standing at distinct locations $(x_1, y_1) \ldots (x_n, y_n)$ on his two-dimensional farm ($1 \leq N \leq 1000$, and the $x_i$'s and $y_i$'s are positive odd integers of size at most $1,000,000$). FJ wants to partition his field by building a long (effectively infinite-length) north-south fence with equation $x=a$ ($a$ will be an even integer, thus ensuring that he does not build the fence through the position of any cow). He also wants to build a long (effectively infinite-length) east-west fence with equation $y=b$, where $b$ is an even integer. These two fences cross at the point $(a,b)$, and together they partition his field into four regions. FJ wants to choose $a$ and $b$ so that the cows appearing in the four resulting regions are reasonably "balanced", with no region containing too many cows. Letting $M$ be the maximum number of cows appearing in one of the four regions, FJ wants to make $M$ as small as possible. Please help him determine this smallest possible value for $M$. 给你一个矩阵,里面有些点,让你横向切一刀,纵向切一刀,使得得到的四个区域内的最大的点数最少。



The first line of the input contains a single integer, $N$. The next $N$ lines each contain the location of a single cow, specifying its $x$ and $y$ coordinates.


You should output the smallest possible value of $M$ that FJ can achieve by positioning his fences optimally.


输入样例 #1

7 3
5 5
7 13
3 1
11 7
5 3
9 1

输出样例 #1