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

 cow.

Write a single line of output containing the maximum number of cows a broadcast from a single cow ca