{"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\"\u003e Teacher Mai has a kingdom with the infinite area.\u003cbr\u003e\u003cbr\u003e He has n students guarding the kingdom.\u003cbr\u003e\u003cbr\u003e The i-th student stands at the position (x\u003csub\u003ei\u003c/sub\u003e,y\u003csub\u003ei\u003c/sub\u003e), and his walking speed is v\u003csub\u003ei\u003c/sub\u003e.\u003cbr\u003e\u003cbr\u003e If a point can be reached by a student, and the time this student walking to this point is \u003cb\u003estrictly less\u003c/b\u003e than other students, this point is in the charge of this student.\u003cbr\u003e\u003cbr\u003e For every student, Teacher Mai wants to know if the area in the charge of him is infinite.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":" There are multiple test cases, terminated by a line \"0\".\u003cbr\u003e\u003cbr\u003e For each test case, the first line contains one integer n(1\u0026lt;\u003dn\u0026lt;\u003d500).\u003cbr\u003e\u003cbr\u003e In following n lines, each line contains three integers x\u003csub\u003ei\u003c/sub\u003e,y\u003csub\u003ei\u003c/sub\u003e,v\u003csub\u003ei\u003c/sub\u003e(0\u0026lt;\u003d|x\u003csub\u003ei\u003c/sub\u003e|,|y\u003csub\u003ei\u003c/sub\u003e|,v\u003csub\u003ei\u003c/sub\u003e\u0026lt;\u003d10^4)."}},{"title":"Output","value":{"format":"HTML","content":" For each case, output \"Case #k: s\", where k is the case number counting from 1, and s is a string consisting of n character. If the area in the charge of the i-th student isn\u0027t infinite, the i-th character is \"0\", else it\u0027s \"1\"."}},{"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\u003e3\r\n0 0 3\r\n1 1 2\r\n2 2 1\r\n0\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 100\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}