Load Balancing
Farmer John's N cows are each standing at distinct locations (x1,y1)…(xn,yn) on his two-dimensional farm (1≤N≤100,000, and the xi's and yi'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.
Problem credits: Brian Dean
Source: USA Computing Olympiad.
Input Format
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.
Output Format
You should output the smallest possible value of M that FJ can achieve by positioning his fences optimally.