{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou are given a set of points in 3-D space. Your task is to calculate the number of \u003cstrong\u003ek\u003c/strong\u003e vertex sides of the convex polyhedron with minimal volume that contains the whole given set of points.\u003c/p\u003e\n\n\u003cp\u003e\u003ch2\u003eInput\u003c/h2\u003e\u003c/p\u003e\n\n\u003cp\u003eFirst line of input contains the quantity of tests \u003cstrong\u003eT\u003c/strong\u003e (\u003cstrong\u003e1\u003c/strong\u003e ≤ \u003cstrong\u003eT\u003c/strong\u003e ≤ \u003cstrong\u003e100\u003c/strong\u003e). First line of each test case contains the number of points in given set \u003cstrong\u003eN\u003c/strong\u003e (\u003cstrong\u003e4\u003c/strong\u003e ≤ \u003cstrong\u003eN\u003c/strong\u003e ≤ \u003cstrong\u003e30\u003c/strong\u003e). Then \u003cstrong\u003eN\u003c/strong\u003e lines follow, each of which contains \u003cstrong\u003e3\u003c/strong\u003e integer numbers: \u003cstrong\u003eX\u003c/strong\u003e, \u003cstrong\u003eY\u003c/strong\u003e, \u003cstrong\u003eZ\u003c/strong\u003e (\u003cstrong\u003e--1000\u003c/strong\u003e ≤ \u003cstrong\u003eX\u003c/strong\u003e, \u003cstrong\u003eY\u003c/strong\u003e, \u003cstrong\u003eZ\u003c/strong\u003e ≤ \u003cstrong\u003e1000\u003c/strong\u003e) -- coordinates of points. Some points can have the same coordinates! It’s guaranteed, that any convex polyhedron, that contains all given points, has a positive volume.\u003c/p\u003e\n\n\u003cp\u003e\u003ch2\u003eOutput\u003c/h2\u003e\u003c/p\u003e\n\n\u003cp\u003eFor each of \u003cstrong\u003eT\u003c/strong\u003e test cases output a line of the form \"\u003cstrong\u003eCase\u003c/strong\u003e #\u003cstrong\u003eA\u003c/strong\u003e:\", where \u003cstrong\u003eA\u003c/strong\u003e is the number of test (beginning from \u003cstrong\u003e1\u003c/strong\u003e), and then -- \u003cstrong\u003eM\u003c/strong\u003e more lines, where \u003cstrong\u003eM\u003c/strong\u003e is the quantity of different side types (a side type means quantity of its vertices). In each of the next \u003cstrong\u003eM\u003c/strong\u003e lines you have to output two numbers: \u003cstrong\u003ek\u003c/strong\u003e -- the number of vertices in the side and \u003cstrong\u003eq_k\u003c/strong\u003e -- the number of \u003cstrong\u003ek\u003c/strong\u003e vertex sides in the polyhedron. After \u003cstrong\u003ek\u003c/strong\u003e you must print a colon \":\" and then -- a space. You have to output the result in ascending order of \u003cstrong\u003ek\u003c/strong\u003e. The quantity of vertices in a side is determined only by geometrical meanings. That is, if a given point lies on an edge of a side, it mustn’t be considered as a vertex, and if some such point lie in one vertex, they must be considered as a single vertex.\u003c/p\u003e\n\n"}},{"title":"Example","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\u003e2\n6\n0 0 0\n2 0 0\n0 2 0\n2 2 0\n3 1 0\n1 1 1\n5\n0 0 0\n1 1 0\n0 2 0\n2 1 0\n1 1 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1:\n3: 5\n5: 1\nCase #2:\n3: 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}