## USACO 2016 February Contest, Bronze

## Problem 3. Load Balancing

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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 ($1 \leq N \leq 100$,
and the $x_i$'s and $y_i$'s are positive odd integers of size at most $B$). 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.

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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 $M$.

For the first five test cases, $B$ is guaranteed to be at most 100. In all test cases, $B$ is guaranteed to be at most 1,000,000.

#### INPUT FORMAT (file balancing.in):

The first line of the input contains two integers, $N$ and $B$. The next $n$ lines each contain the location of a single cow, specifying its $x$ and $y$ coordinates.#### OUTPUT FORMAT (file balancing.out):

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

7 10 7 3 5 5 9 7 3 1 7 7 5 3 9 1

#### SAMPLE OUTPUT:

2

Problem credits: Brian Dean