{"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\"\u003eAs this term is going to end, DRD needs to start his graphical homework.\u003cbr\u003e\u003cbr\u003eIn his homework, DRD needs to partition a point set $S$ into two part. You can see that if one part has 100 points and the other has only 1 point, then this partition cannot be beautiful since it\u0027s too imbalanced. DRD wants to find a line to separate $S$, so that no points lie in the line and there are at least $\\lfloor \\frac{|S|}{3}\\rfloor$ points in each side of the line. DRD finds it amazing that there may exist some points (no need to be in $S$) that if a line $l$ passes it and does not pass any points in $S$, then $l$ can be a separating line. Now, he wonders the area these points form. \u003cbr\u003e\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"First line: a positive integer $T \\leq 10$ indicating the number of test cases.\u003cbr\u003eThere are $T$ cases following. In each case, the first line contains an positive integer $n \\leq 1000$, and $n$ lines follow. In each of these lines, there are 2 integers $x_i, y_i$ indicating a point $(x_i, y_i)$ in the plane. Note that $|x_i|, |y_i| \\leq 10^4$\u003cbr\u003eYou can assume that no three points in $S$ lies in the same line. \u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case: output \u0027\u0027Case #x: ans\u0027\u0027 (without quotes), where $x$ is the number of the cases, and $ans$ is the area these points form.\u003cbr\u003eYour answer is considered correct if and only if the absolute error or the relative error is smaller than $10^{-6}$. \u003cbr\u003e\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\u003e2\r\n4\r\n1 1\r\n1 -1\r\n-1 -1\r\n-1 1\r\n8\r\n-1 -1\r\n-1 1\r\n1 -1\r\n1 1\r\n-2 -2\r\n-2 2\r\n2 -2\r\n2 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 4.000000\r\nCase #2: 5.333333\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}