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.
You must sign in to write code.