{"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\"\u003eCoffee Chicken has started a new restaurant named Pizza Hu...b! It provides various styles of pizzas, hamburgers, sandwiches, coffee, chickens and many other awesome Western cuisines. Welcome to Pizza Hub after this Multi-University Training Contest!\u003cbr\u003e\u003cbr\u003eSince the pizzas are so exquisite, it is never a bad thing to design nice paper pads for them. The pizzas provided in Pizza Hub are sliced into triangles. The rectangular-shaped paper pads are cut from a paper strip of fixed width which is long enough. The pizza should be placed entirely on the pad; however, their borders are allowed to touch. Also, you are allowed to rotate the pizza.\u003cbr\u003e\u003cbr\u003eAs the customized paper strip is rather expensive, minimizing the size of the pizza pad can save a lot of money. Can you determine the minimum possible height of the pizza pad, given the width of the paper strip? The following picture illustrates the first sample test case.\u003cbr\u003e\u003cbr\u003e\u003ccenter\u003e\u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/736d9b1fcce1732579c8b714992de560?v\u003d1715075397\"\u003e\u003c/center\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input is a single integer $T$ $(1 \\leq T \\leq 50000)$, the number of test cases.\u003cbr\u003e\u003cbr\u003eEach test case is a single line of seven integers $x_1, y_1, x_2, y_2, x_3, y_3$ $(0 \\leq x_1, y_1, x_2, y_2, x_3, y_3 \\leq 10000)$ and $w$ $(1 \\leq w \\leq 10000)$, where $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ are Cartesian coordinates of the vertices of the pizza, and $w$ is the width of the strip. It is guaranteed that the three vertices are not collinear. "}},{"title":"Output","value":{"format":"HTML","content":"For each test case, display the minimum height of the pizza pad with an absolute or relative error of no more than $10^{-6}$. If it is impossible to make a pizza pad, display $\\texttt{impossible}$ instead.\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\n0 0 3 0 0 4 10\r\n0 0 3 0 0 4 1\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2.400000000\r\nimpossible\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}