A889. Load Balancing--Bronze

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 $M$.

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.