{"trustable":true,"prependHtml":"\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eAlice is interesting in computation geometry problem recently. She found a interesting problem and solved it easily. Now she will give this problem to you :\u003cbr\u003e\u003cbr\u003eYou are given $N$ distinct points $(X_i,Y_i)$ on the two-dimensional plane. Your task is to find a point $P$ and a real number $R$, such that for at least $\\lceil \\frac{N}{2} \\rceil$ given points, their distance to point $P$ is equal to $R$.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line is the number of test cases.\u003cbr\u003e\u003cbr\u003eFor each test case, the first line contains one positive number $N(1 \\leq N \\leq 10^5)$.\u003cbr\u003e\u003cbr\u003eThe following $N$ lines describe the points. Each line contains two real numbers $X_i$ and $Y_i$ $(0 \\leq |X_i|, |Y_i| \\leq 10^3)$ indicating one give point. It\u0027s guaranteed that $N$ points are distinct.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output a single line with three real numbers $X_P, Y_P, R$, where $(X_P,Y_P)$ is the coordinate of required point $P$. \u003cb\u003eThree real numbers you output should satisfy $0 \\leq |X_P|, |Y_P|, R \\leq 10^9$.\u003c/b\u003e\u003cbr\u003e\u003cbr\u003eIt is guaranteed that there exists at least one solution satisfying all conditions. And if there are different solutions, print any one of them. The judge will regard two point\u0027s distance as $R$ if it is within an absolute error of $10^{-3}$ of $R$.\u003cbr\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\u003e1\r\n7\r\n1 1\r\n1 0\r\n1 -1\r\n0 1\r\n-1 1\r\n0 -1\r\n-1 0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0 0 1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}