UFO#2201
In the small town, the M Control Service for unlawful UFO flights has begun to operate. The first task of the service is to find out how many UFOs are operating in the vicinity of the city.
Service agents interviewed many witnesses and compiled a list of UFO encounters that took place during one day, indicating the location and time of each sighting.
Now, analysts want to understand how many UFOs there actually were. According to intelligence data, the maximum speed at which a UFO can fly is known. Analysts are asking you to determine the minimum number of UFOs that witnesses could have observed.
The first line of the input file contains integers and — the number of sightings and the maximum speed of a UFO (1 \leq n \leq 100, 1 \leq v \leq 10000). The following lines contain descriptions of the UFO encounters in the format " ", where is the time of the encounter, and , are the coordinates of the location where the UFO was observed (for simplicity, assume all encounters took place on a plane). The absolute values of the coordinates do not exceed .
The speed is given in km/h, and the coordinates are in km.
Output a single number — the minimum possible number of UFOs.
Example 1