{"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 You are now working in a physical laboratory. One day, when you were skimming through your records of experiments, you find that the squared frequency, defined as (P/Q)\u003csup\u003e2\u003c/sup\u003e, in which Q indicates times of experiments and P means number of experiments in which the expected phenomenon appears, is somehow unreasonable. The squared frequency F (0 \u0026lt; F \u0026lt; 1) is written in decimal form, and rounded to K (K ≤ 9) numbers after the decimal point. You think that Q, i.e. times of experiments, is too small to obtain such a number. Now you need to work out a fraction P/Q, so that rounding (P/Q)\u003csup\u003e2\u003c/sup\u003e to K numbers after the decimal point gets exactly F, and minimizes Q. \u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":" Input contains no more than 2000 test cases. \u003cbr\u003e\u003cbr\u003e Each test case has a single line, which contains a decimal fraction indicating F, the squared frequency."}},{"title":"Output","value":{"format":"HTML","content":" For each test case, output your answer in a line with the case number, follow the format in sample. You should print a blank after \u0027:\u0027.\u003cbr\u003e\u003cbr\u003e If the answer is not unique, output the one with the minimum P."}},{"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\u003e0.3\r\n0.5\r\n0.50\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 1/2\r\nCase #2: 5/7\r\nCase #3: 12/17\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}