B'The Cybermen have again outwitted the Daleks! Unfortunately, this time the Daleks decided to abandon these tasks altogether, which means the Doctor has to deal with them. The Doctor can handle the Daleks on his own, but Heidi now has to make sure that the Cybermen are kept busy with this next task. There are k rings on a plane. For each ring, n points are uniformly sampled with a small random noise. The task is to recover the rings given only the noisy samples. The rings and the samples are generated as follows. The center of a ring is uniformly sampled from a disk of radius 1 ,000 ,000 centered at the origin, and the radius of the ring is uniformly sampled from [250 ,000, 750 ,000] . Let R be a ring with center (x, y) and radius r . To sample a point from R , an angle theta is uniformly sampled from [0, 2 pi] and a distance d is uniformly sampled from [0.9r, 1.1r] . The coordinates of the sampled point are then (x+d cos( theta), y+d sin( theta)) rounded to the closest integers. The distance between rings is measured by their Hausdorff distance. In our case, the distance between two rings R_1, R_2 can be written as follow. Let d be the distance between the two centers and r_1, r_2 be the radii. Then the distance is dist(R_1, R_2)= max( min(d_{--}, d_{-+}), min(d_{+-}, d_{++}), min(d_{--}, d_{+-}), min(d_{-+}, d_{++})) , where d_{++}=|d+r_1+r_2| , d_{+-}=|d+r_1-r_2| , d_{-+}=|d-r_1+r_2| , d_{--}=|d-r_1-r_2| . We say that a ring R_0 is recovered if one of the rings R in the output has Hausdorff distance less than 100 ,000 from R_0 . An output is accepted if all the rings are recovered. It is guaranteed that the distances between any two rings is greater than 600 ,000 . Remember that a human can very easily solve this task, so make sure that no human traitors are helping the Cybermen complete this task. The'...