Liam (angryneeson52) is playing his favorite tower defense
game! This game involves destroying minions of his opponent
while defending his own villages.
Liam’s favorite attack is an Area of Effect attack. The Area
of Effect attack is a perfect circle. Liam simply picks a
center and a radius for the attack and every minion in or on
that circle gets destroyed! Minions are small enough to be
considered points.
The game isn’t as simple as just destroying all minions.
Liam must also avoid hitting his villages with his attacks. The
attack may touch the walls of a village but must not enter the
village. Villages are also perfect circles.
His attack also has a limit on its maximum radius. The
attack can be reduced in radius but cannot go above the
maximum.
Determine the maximum number of minions Liam can destroy in
a single attack without damaging any of his own villages.
Input
Each input will consist of a single test case. Note that
your program may be run multiple times on different inputs.
Each input begins with a line with 3 spaceseparated integers,
$n\ m\ r$, where:

$n$ ($1\le n \le 10$) is the number of
Liam’s villages

$m$ ($1 \le m \le 2\, 000$) is the
number of opposing minions

$r$ ($1 \le r \le 20\, 000$) is the
maximum radius of Liam’s Area of Effect attack
The next $n$ lines will
each contain 3 spaceseparated integers $vx\ vy\ vr$ which represent the
location ($20\, 000\le vx, vy
\le 20\, 000$) and radius ($1\le vr \le 20\, 000$) of one of
Liam’s villages. No two villages will intersect or overlap.
The next $m$ lines will
each contain 2 spaceseparated integers $mx\ my$ which represent the location
($20\, 000 \le mx, my \le 20\,
000$) of one of the enemy minions. No two minions will
occupy the same point, and no enemy minion will be inside any
of Liam’s villages.
Output
Output a single integer representing the maximum number of
enemy minions that Liam can destroy with a single attack.
Sample Input 1 
Sample Output 1 
1 3 3
0 0 1
3 3
3 3
3 3

1

Sample Input 2 
Sample Output 2 
1 5 3
0 0 1
3 3
3 3
3 3
3 0
0 3

3

Sample Input 3 
Sample Output 3 
4 10 100
0 0 3
10 0 3
10 10 3
0 10 3
0 4
0 5
0 6
5 3
5 3
5 5
6 7
3 6
10 4
8 4

5
