Cloudlet
The factory has received an order to create a stencil for stamping clouds on cheerful posters. This stencil is made from a rectangular steel sheet measuring 100000×100000 millimeters. A drilling machine with programmed control will drill several round holes into the sheet to form a specific shape (as illustrated). Fedor Ivanovich, a programmer, developed a program for the machine that successfully completes this task, and he was very pleased with his work. However, in the evening, his son Borenka, a student at a local lyceum, visited the workshop. Borenka was surprised by the program's size and pointed out to his father that the same illustration could be achieved with far fewer operations.
Your task is to develop a program that determines the maximum number of commands that can be removed from Fedor Ivanovich's program while keeping the illustration unchanged.
Input
The first line of the input file contains the number n (0 ≤ n ≤ 200) — the number of commands in Fedor Ivanovich's program. The following n lines contain the descriptions of these commands. Each command is described on a separate line and consists of three numbers, separated by spaces — the coordinates of the center of the hole and the radius of the drill to be used. All numbers in the file are real. Measurements are in millimeters. The origin of the coordinate system is at the upper left corner of the sheet, with the OX axis extending to the right and the OY axis extending downward. It is guaranteed that the illustration's area is simply connected, all holes are strictly within the sheet, no two circles touch or coincide, and no three circles intersect at a single point. The distances between intersection points of the circles are at least 0.0001 mm.
Output
Output the maximum number of commands that can be removed from Fedor Ivanovich's program while ensuring the illustration remains unchanged.