{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eProbably, you visited airports in which airplanes take off every minute or even more frequently. And did you ever imagine how many airplanes there are in the air simultaneously? And what about the whole globe?\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eAssume that the Earth is an ideal ball with center at (0, 0, 0) and radius 6370 kilometers.\r\nMost passenger planes fly at a height not more than 15 \r\nkilometers. If you could look at the Earth from the outside,\r\nthe planes would look as points on its surface. Suppose that at \r\nsome moment there are \u003ci\u003eN\u003c/i\u003e planes in the air. A plane number\r\n\u003ci\u003ei\u003c/i\u003e is at the point of intersection of the Earth sphere\r\nwith the ray starting at the origin and having directing vector\r\n(\u003ci\u003eX\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e, \u003ci\u003eY\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e, \u003ci\u003eZ\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e). \r\nThere is not more than one plane at each point of the Earth\u0027s \r\nsurface. You task is to determine the maximal number of planes \r\nthat can be seen simultaneously from a very large distance from \r\nthe Earth. From this distance, an open hemisphere of the Earth\u0027s surface can be observed.\r\n\u003c/div\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eThe first line contains an integer \u003ci\u003eN\u003c/i\u003e (1 ≤ \u003ci\u003eN\u003c/i\u003e ≤ 150). \r\nThe next \u003ci\u003eN\u003c/i\u003e lines contain triples of integers \u003ci\u003eX\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e, \r\n\u003ci\u003eY\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e, \u003ci\u003eZ\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e, which are directing vectors\r\nof the rays passing through the planes. The absolute values of \r\nthese numbers do not exceed 600, and each triple contains at least one nonzero number. \r\n\u003c/div\u003e\u003c/div\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eYou should output the maximal number of planes that can be seen simultaneously from a very large distance from the Earth.\u003c/div\u003e\u003c/div\u003e"}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e6\r\n0 0 1\r\n0 0 -1\r\n0 1 0\r\n0 -1 0\r\n1 0 0\r\n-1 0 0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}