Gold Mines
Bateman, a distinguished employee of the gold mining company in Bateland, is retiring this year. To honor his service, the company management has decided to reward him. Bateman is allowed to select a rectangular plot of land with dimensions s and w, aligned with the coordinate axes, and claim all the mines located within or on the boundary of this plot. He has the freedom to choose the location of this plot. The value of the plot is defined as the number of mines it encompasses, including those on its boundary.
Your task is to determine the maximum possible value of such a plot.
Input
The first line of input provides the integers s and w (1 ≤ s, w ≤ 10000), which represent the lengths of the plot's sides parallel to the OX and OY axes, respectively.
The second line contains the integer N, the number of mines (1 ≤ N ≤ 15000). The next N lines each contain a pair of integers, representing the coordinates of a mine, with each coordinate not exceeding 30000 in absolute value.
Output
Output a single number: the maximum number of mines that can be included on the plot.