Apple from the tree...#1742
Petya has an apple tree in his garden. Inspired by the story of Isaac Newton, who is known to have discovered the law of universal gravitation after an apple fell on his head, Petya often sits under the apple tree to improve his performance in physics.
However, since Petya's grade in physics is barely a three, apples from his tree fall in the following way. At some moment, one of the apples detaches from the branch on which it hangs and begins to fall straight down. If at any moment it touches another apple, that apple also detaches from its branch and begins to fall downward, while the first apple continues to fall straight down without changing its direction. In general, if any falling apple touches another apple on its way, the latter also begins to fall.
Thus, at any time, each apple is either hanging on the branch or falling straight down. Furthermore, except for the first apple, any apple must first come into contact with another falling apple before it starts to fall.
Determine which apples will fall from Petya's tree.
The first line contains — the number of apples on Petya's apple tree (1 \le N \le 200). The next lines contain descriptions of the apples. All apples are considered to be spheres. Each apple is given by the coordinates of its uppermost point (the point where it was originally attached to the tree, with the length of the stem neglected) x_i, y_i, and z_i, as well as its radius r_i (-10000 \le x_i, y_i, z_i \le 10000, 1 \le r_i \le 10000; all numbers are integers). It is guaranteed that initially, no apples intersect (not even touch). The axis is directed upward.
Print in the first line the number of apples that will fall from the tree if the first apple starts to fall. On the next line, print the numbers of the apples that have fallen. Apples are numbered starting from in the order in which they are given in the input file.
Example 1