Express delivery#4381
Your company, Byteland Express, has to deliver some parcels to clients located somewhere in the city. The city consist of 2 \cdot 10^9 + 1 south-north streets and 2 \cdot 10^9 + 1 west-east streets (both numbered from to 2 \cdot 10^9). A postman drives from one junction to a neighbouring one in one minute. The company is located next to the junction of streets number x_c and y_c.
All parcels have to be delivered as fast as possible, so driving to a client located next to the junction of the -th and -th street, can take at most (= exactly) |x_c - x| + |y_c - y| minutes. It takes a very short time to give a parcel to a client, so while driving to one client, a postman can give a parcel to another client (but can not choose longer route to do that). Your task is to determine how many postmen are needed to perform the delivery.
Task
Write a program, that
reads using SVIO the position of the company and positions of all the clients,
finds the minimal number of postmen needed to deliver all the parcels,
writes the result using SVIO.
First line of input contains one integer (1 \leq N \leq 1000000). Second line contains location of the company, the following lines contain locations of the clients. A description of the location consists of two integers: coordinates and (0 \leq x, y \leq 2 \cdot 10^9). Every two points (from among company or clients) differ on both coordinates (every is different and every is different).
In the only line of the standard output write one integer: the number of postmen needed to deliver parcels to all clients.
Example 1