#4749. [Usaco2016 Dec]Moocast

内存限制:128 MiB 时间限制:10 Sec


Farmer John's N cows (1≤N≤200) want to organize an emergency "moo-cast" system for broadcasting im
portant messages among themselves.Instead of mooing at each-other over long distances, the cows deci
de to equip themselves with walkie-talkies, one for each cow. These walkie-talkies each have a limit
ed transmission radius -- a walkie-talkie of power PP can only transmit to other cows up to a distan
ce of PP away (note that cow A might be able to transmit to cow B even if cow B cannot transmit back
, due to cow A's power being larger than that of cow B). Fortunately, cows can relay messages to one
-another along a path consisting of several hops, so it is not necessary for every cow to be able to
 transmit directly to every other cow.Due to the asymmetrical nature of the walkie-talkie transmissi
on, broadcasts from some cows may be more effective than from other cows in their ability to reach l
arge numbers of recipients (taking relaying into account). Please help the cows determine the maximu
m number of cows that can be reached by a broadcast originating from a single cow.


The first line of input contains N.The next N lines each contain the xx and yy coordinates of a sing
le cow ( integers in the range 0…25,000) followed by p, the power of the walkie-talkie held by this


Write a single line of output containing the maximum number of cows a broadcast from a single cow ca
n reach. The originating cow is included in this number.



1 3 5
5 4 3
7 2 1
6 1 1


In the example above, a broadcast from cow 1 can reach 3 total cows, including cow 1.