Moocast (Silver)#10561
Farmer John's cows want to set up an emergency "moo-cast" system for broadcasting important messages among themselves.
Instead of mooing to one another over long distances, the cows decide to equip themselves with walkie-talkies, one for each cow. Each walkie-talkie has a limited transmission range: a walkie-talkie with power can transmit to other cows located at a distance of at most away. Note that cow may be able to transmit to cow even if cow cannot transmit back, since cow 's walkie-talkie may have greater power than cow 's.
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 asymmetric nature of walkie-talkie transmission, broadcasts originating from some cows may be more effective than those from others at reaching a large number of recipients, taking message relaying into account. Please help the cows determine the maximum number of cows that can be reached by a broadcast originating from a single cow.
The first line contains n~(1 \le n \le 200). The next lines each contain the and coordinates of a cow (integers in the range from to ), followed by , the power of the walkie-talkie held by that cow.
Print the maximum number of cows that can be reached by a broadcast originating from a single cow. The originating cow is included in this number.
Example 1