Laser#615
Vasya received many balloons and a toy laser as a birthday gift. The balloons are inflated and scattered around the room. Vasya wants to know how many balloons he can pop by firing in a direction of his choice (if only the laser were real!). The laser beam continues in its direction after piercing a balloon. Assume Vasya is an infinitesimal point, and the balloons are circles. Help Vasya.
The program reads from input the number of balloons (1 \leq n \leq 1000), then two integers , (-1000 \leq dx, dy \leq 1000), not both zero, which are the coordinates of a point through which the laser beam will pass. Then, for each of the balloons, the program reads three integers, each with absolute value at most . Each triple consists of the center coordinates and the radius of the balloon (the radius is always positive). Vasya is at the origin. No two balloons overlap, and Vasya is not inside any balloon.
Output the number of balloons pierced by the laser beam. If the laser only touches a balloon, it is not considered pierced.
Example 1