Laser
Vasya received numerous balloons and a toy laser for his birthday. The balloons are inflated and scattered throughout the room. Vasya is curious to find out how many balloons he can pop by aiming the laser in a direction of his choice (if only the laser were real!). The laser beam continues through any balloon it pierces. Assume Vasya is an infinitesimally small point, and the balloons are perfect circles. Help the birthday boy determine the number of balloons he can pop.
Input
The program reads from the input the number of balloons, n (1 ≤ n ≤ 1000), followed by two integers, dx and dy, which are not both zero (-1000 ≤ dx, dy ≤ 1000). These integers represent the coordinates of the direction through which the laser beam will pass. Then, the program reads n sets of three integers, each not exceeding 1000 in absolute value. Each set consists of the coordinates of the center and the radius of a balloon (the radius is always a positive number). Vasya is positioned at the origin. No two balloons overlap, and Vasya is not inside any balloon.
Output
The program should output the number of balloons pierced by the laser beam. If the beam merely touches a balloon, that balloon is not considered pierced.