{"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\"\u003eGenerate three integers $a$, $b$, and $c$ in $[1,n]$ with equal probability independently, and use them as the three right-angle side length of a right-angled tetrahedron. Find the expectation of the \u003cb\u003ereciprocal square\u003c/b\u003e of the distance from the right-angle apex to the slope (Euclidean distance).\u003cbr\u003e\u003cbr\u003eFor each test case, output a line containing the answer mod $998244353$.\u003cbr\u003e\u003cbr\u003e\u003ccenter\u003e\u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/dbbb63d7d0b9744aafcce37c50f9a495?v\u003d1726112499\"\u003e\u003c/center\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"In the first line, you should read an integer $T$ denoting the number of test cases.\u003cbr\u003e\u003cbr\u003eIn every test case, the only line will include an integer $n$.\u003cbr\u003e\u003cbr\u003eIt is guaranteed that $T$ is no larger than $2 \\times 10^6$ and $n$ is no larger than $6 \\times 10^6$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output the only line containing just one integer denoting the answer mod $998244353$."}},{"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\n1\r\n2\r\n3\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n124780546\r\n194103070\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}