{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cbr\u003eTwo circles are \u003ci\u003eorthogonal\u003c/i\u003e, if they intersect and for any point of intersection their tangent lines at that point are perpendicular.\u003cbr\u003eConsider a set of \u003ci\u003en\u003c/i\u003e circles on the plane. You are to find a circle orthogonal to all of them.\u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eInput\u003c/b\u003e\u003c/div\u003eThe input file contains an integer \u003ci\u003en\u003c/i\u003e (1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup\u003e5\u003c/sup\u003e), followed by \u003ci\u003en\u003c/i\u003e triples of integers: \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003er\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, denoting the center coordinates and the radii of the circles (-10\u003csup\u003e6\u003c/sup\u003e ≤ \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup\u003e6\u003c/sup\u003e, 1 ≤ \u003ci\u003er\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup\u003e6\u003c/sup\u003e).\u003cbr\u003eThe circles may coincide.\u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eOutput\u003c/b\u003e\u003c/div\u003eIf there exists exactly one circle orthogonal to all the given ones, output its center coordinates and radius as real numbers separated with single spaces. The numbers will be considered correct if they are within 10\u003csup\u003e-6\u003c/sup\u003e relative or absolute error of the exact answers.\u003cbr\u003eIn case there\u0027s no such circle, output -1. In case there are many, output -2. \u003cbr\u003e"}},{"title":"Sample 1","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\u003e3\n0 0 5\n7 16 10\n10 0 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5.0 5.0 5.0\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003cbr\u003e\nThe example is illustrated by the following picture:\n\u003cbr\u003e\u003cimg src\u003d\"CDN_BASE_URL/67f5993a1bb220cedf8c60e15714c699?v\u003d1715378378\" style\u003d\"vertical-align: text-bottom;top: -2.0px;max-width: 100.0%;max-height: 100.0%;\"\u003e\n\u003cbr\u003e"}}]}