{"trustable":false,"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":"\u003cscript type\u003d\u0027text/x-mathjax-config\u0027\u003eMathJax.Hub.Config({tex2jax: { inlineMath: [[\u0027$\u0027,\u0027$\u0027]] } }); \u003c/script\u003e\n\u003cscript type\u003d\u0027text/javascript\u0027 src\u003d\u0027https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\u0027\u003e\u003c/script\u003e\n\u003cscript type\u003d\u0027text/javascript\u0027\u003esetTimeout(function(){MathJax.Hub.Queue([\u0027Typeset\u0027, MathJax.Hub, \u0027left_view\u0027]);}, 2000);\u003c/script\u003e\n\u003cdiv class\u003d\"panel_content\"\u003e\n On an infinite smooth table, there\u0027s a big round fixed cylinder and a little ball whose volume can be ignored. \n \u003cbr\u003e \n \u003cbr\u003eCurrently the ball stands still at point $A$, then we\u0027ll give it an initial speed and a direction. If the ball hits the cylinder, it will bounce back with no energy losses. \n \u003cbr\u003e \n \u003cbr\u003eWe\u0027re just curious about whether the ball will pass point $B$ after some time. \n\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"First line contains an integer $T$, which indicates the number of test cases. \n\u003cbr\u003e \n\u003cbr\u003eEvery test case contains three lines. \n\u003cbr\u003e \n\u003cbr\u003eThe first line contains three integers $O_x$, $O_y$ and $r$, indicating the center of cylinder is $(O_x, O_y)$ and its radius is $r$. \n\u003cbr\u003e \n\u003cbr\u003eThe second line contains four integers $A_x$, $A_y$, $V_x$ and $V_y$, indicating the coordinate of $A$ is $(A_x, A_y)$ and the initial direction vector is $(V_x, V_y)$. \n\u003cbr\u003e \n\u003cbr\u003eThe last line contains two integers $B_x$ and $B_y$, indicating the coordinate of point $B$ is $(B_x, B_y)$. \n\u003cbr\u003e \n\u003cbr\u003e$\\cdot$ 1 ≤ $T$ ≤ 100. \n\u003cbr\u003e \n\u003cbr\u003e$\\cdot$ |$O_x$|,|$O_y$|≤ 1000. \n\u003cbr\u003e \n\u003cbr\u003e$\\cdot$ 1 ≤ $r$ ≤ 100. \n\u003cbr\u003e \n\u003cbr\u003e$\\cdot$ |$A_x$|,|$A_y$|,|$B_x$|,|$B_y$|≤ 1000. \n\u003cbr\u003e \n\u003cbr\u003e$\\cdot$ |$V_x$|,|$V_y$|≤ 1000. \n\u003cbr\u003e \n\u003cbr\u003e$\\cdot$ $V_x \\neq 0$ or $V_y \\neq 0$. \n\u003cbr\u003e \n\u003cbr\u003e$\\cdot$ both A and B are outside of the cylinder and they are not at same position."}},{"title":"Output","value":{"format":"HTML","content":"For every test case, you should output \" \n\u003cb\u003eCase #x: y\u003c/b\u003e\", where $x$ indicates the case number and counts from $1$. $y$ is \" \n\u003cb\u003eYes\u003c/b\u003e\" if the ball will pass point $B$ after some time, otherwise $y$ is \" \n\u003cb\u003eNo\u003c/b\u003e\"."}},{"title":"Sample Input","value":{"format":"HTML","content":"\u003cpre\u003e2\n0 0 1\n2 2 0 1\n-1 -1\n0 0 1\n-1 2 1 -1\n1 2\u003c/pre\u003e"}},{"title":"Sample Output","value":{"format":"HTML","content":"\u003cpre\u003eCase #1: No\nCase #2: Yes\u003c/pre\u003e"}}]}